{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T15:15:16Z","timestamp":1770909316911,"version":"3.50.1"},"reference-count":59,"publisher":"American Mathematical Society (AMS)","issue":"2","license":[{"start":{"date-parts":[[2004,8,21]],"date-time":"2004-08-21T00:00:00Z","timestamp":1093046400000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Trans. Amer. Math. Soc."],"abstract":"

We initiate the study of the class of profinite graphs\u0393<\/mml:mi>\\Gamma<\/mml:annotation><\/mml:semantics><\/mml:math><\/inline-formula>defined by the following geometric property: for any two verticesv<\/mml:mi>v<\/mml:annotation><\/mml:semantics><\/mml:math><\/inline-formula>andw<\/mml:mi>w<\/mml:annotation><\/mml:semantics><\/mml:math><\/inline-formula>of\u0393<\/mml:mi>\\Gamma<\/mml:annotation><\/mml:semantics><\/mml:math><\/inline-formula>, there is a (unique) smallest connected profinite subgraph of\u0393<\/mml:mi>\\Gamma<\/mml:annotation><\/mml:semantics><\/mml:math><\/inline-formula>containing them; such graphs are calledtree-like<\/italic>. Profinite trees in the sense of Gildenhuys and Ribes are tree-like, but the converse is not true. A profinite group is then said to bedendral<\/italic>if it has a tree-like Cayley graph with respect to some generating set; a Bass-Serre type characterization of dendral groups is provided. Also, such groups (including free profinite groups) are shown to enjoy a certain small cancellation condition. We define a pseudovariety of groupsH<\/mml:mi><\/mml:mrow>\\mathbf {H}<\/mml:annotation><\/mml:semantics><\/mml:math><\/inline-formula>to bearboreous<\/italic>if all finitely generated free pro-H<\/mml:mi><\/mml:mrow>\\mathbf {H}<\/mml:annotation><\/mml:semantics><\/mml:math><\/inline-formula>groups are dendral (with respect to a free generating set). Our motivation for studying such pseudovarieties of groups is to answer several open questions in the theory of profinite topologies and the theory of finite monoids. We prove, for arboreous pseudovarietiesH<\/mml:mi><\/mml:mrow>\\mathbf {H}<\/mml:annotation><\/mml:semantics><\/mml:math><\/inline-formula>, a pro-H<\/mml:mi><\/mml:mrow>\\mathbf {H}<\/mml:annotation><\/mml:semantics><\/mml:math><\/inline-formula>analog of the Ribes and Zalesski\u012d product theorem for the profinite topology on a free group. Also, arboreous pseudovarieties are characterized as precisely the solutionsH<\/mml:mi><\/mml:mrow>\\mathbf {H}<\/mml:annotation><\/mml:semantics><\/mml:math><\/inline-formula>to the much studied pseudovariety equation\\mathbf {J}\\ast \\mathbf {H}= \\mathbf {J} \\text {\\textcircled {<\/tex-math><\/inline-formula>m}} \\mathbf {H}<\/tex-math><\/inline-formula>.<\/p>","DOI":"10.1090\/s0002-9947-03-03358-0","type":"journal-article","created":{"date-parts":[[2003,10,16]],"date-time":"2003-10-16T12:27:02Z","timestamp":1066307222000},"page":"805-851","source":"Crossref","is-referenced-by-count":16,"special_numbering":"825","title":["The geometry of profinite graphs with applications to free groups and finite monoids"],"prefix":"10.1090","volume":"356","author":[{"given":"K.","family":"Auinger","sequence":"first","affiliation":[]},{"given":"B.","family":"Steinberg","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2003,8,21]]},"reference":[{"key":"1","series-title":"Series in Algebra","isbn-type":"print","volume-title":"Finite semigroups and universal algebra","volume":"3","author":"Almeida, Jorge","year":"1994","ISBN":"https:\/\/id.crossref.org\/isbn\/9810218958"},{"issue":"3-4","key":"2","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1142\/S0218196799000163","article-title":"Hyperdecidable pseudovarieties and the calculation of semidirect products","volume":"9","author":"Almeida, Jorge","year":"1999","journal-title":"Internat. J. Algebra Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0218-1967","issn-type":"print"},{"issue":"1","key":"3","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1112\/S0024611500012144","article-title":"On the decidability of iterated semidirect products with applications to complexity","volume":"80","author":"Almeida, Jorge","year":"2000","journal-title":"Proc. London Math. Soc. (3)","ISSN":"https:\/\/id.crossref.org\/issn\/0024-6115","issn-type":"print"},{"key":"4","first-page":"1","article-title":"Syntactic and global semigroup theory: a synthesis approach","author":"Almeida, Jorge","year":"2000"},{"issue":"3","key":"5","doi-asserted-by":"publisher","first-page":"375","DOI":"10.1142\/S0218196794000051","article-title":"Reduced factorizations in free profinite groups and join decompositions of pseudovarieties","volume":"4","author":"Almeida, Jorge","year":"1994","journal-title":"Internat. J. Algebra Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0218-1967","issn-type":"print"},{"key":"6","first-page":"73","article-title":"Relatively free profinite monoids: an introduction and examples","author":"Almeida, J.","year":"1995"},{"issue":"1","key":"7","first-page":"3","article-title":"Free profinite semigroups over semidirect products","author":"Alme\u012dda, Zh.","year":"1995","journal-title":"Izv. Vyssh. Uchebn. Zaved. Mat.","ISSN":"https:\/\/id.crossref.org\/issn\/0021-3446","issn-type":"print"},{"issue":"1","key":"8","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1142\/S0218196791000079","article-title":"Inevitable graphs: a proof of the type \ud835\udc3c\ud835\udc3c conjecture and some related decision procedures","volume":"1","author":"Ash, C. J.","year":"1991","journal-title":"Internat. J. Algebra Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0218-1967","issn-type":"print"},{"key":"9","first-page":"25","article-title":"Semigroups with central idempotents","author":"Auinger, Karl","year":"2000"},{"issue":"2-3","key":"10","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1016\/S0022-4049(01)00081-0","article-title":"Join decompositions of pseudovarieties involving semigroups with commuting idempotents","volume":"170","author":"Auinger, K.","year":"2002","journal-title":"J. Pure Appl. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0022-4049","issn-type":"print"},{"issue":"4","key":"11","doi-asserted-by":"publisher","first-page":"433","DOI":"10.1142\/S0218196797000198","article-title":"Congruences on the lattice of pseudovarieties of finite semigroups","volume":"7","author":"Auinger, K.","year":"1997","journal-title":"Internat. J. Algebra Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0218-1967","issn-type":"print"},{"key":"12","series-title":"Mathematical Surveys, No. 7","volume-title":"The algebraic theory of semigroups. Vol. I","author":"Clifford, A. H.","year":"1961"},{"issue":"1-2","key":"13","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1142\/S0218196702000924","article-title":"Combinatorial group theory, inverse monoids, automata, and global semigroup theory","volume":"12","author":"Delgado, Manuel","year":"2002","journal-title":"Internat. J. Algebra Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0218-1967","issn-type":"print"},{"key":"14","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1002\/sapm1939181153","article-title":"A function related to the series for \ud835\udc52^{\ud835\udc52^{\ud835\udc65}}","volume":"18","author":"Epstein, Leo F.","year":"1939","journal-title":"J. Math. Phys. Mass. Inst. Tech.","ISSN":"https:\/\/id.crossref.org\/issn\/0097-1421","issn-type":"print"},{"issue":"3","key":"15","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1016\/S0022-4049(97)00172-2","article-title":"Semigroup expansions using the derived category, kernel, and Malcev products","volume":"136","author":"Elston, Gillian Z.","year":"1999","journal-title":"J. Pure Appl. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0022-4049","issn-type":"print"},{"issue":"6","key":"16","doi-asserted-by":"publisher","first-page":"703","DOI":"10.1142\/S0218196795000288","article-title":"On separability properties of groups","volume":"5","author":"Gitik, Rita","year":"1995","journal-title":"Internat. J. Algebra Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0218-1967","issn-type":"print"},{"issue":"1","key":"17","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/0022-4049(78)90019-1","article-title":"Profinite groups and Boolean graphs","volume":"12","author":"Gildenhuys, Dion","year":"1978","journal-title":"J. Pure Appl. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0022-4049","issn-type":"print"},{"key":"18","doi-asserted-by":"publisher","first-page":"712","DOI":"10.2307\/1968951","article-title":"Rings with minimal condition for left ideals","volume":"40","author":"Hopkins, Charles","year":"1939","journal-title":"Ann. of Math. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0003-486X","issn-type":"print"},{"issue":"5","key":"19","doi-asserted-by":"publisher","first-page":"1985","DOI":"10.1090\/S0002-9947-99-02374-0","article-title":"Extending partial automorphisms and the profinite topology on free groups","volume":"352","author":"Herwig, Bernhard","year":"2000","journal-title":"Trans. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9947","issn-type":"print"},{"issue":"4","key":"20","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1142\/S0218196791000298","article-title":"Ash\u2019s type \ud835\udc3c\ud835\udc3c theorem, profinite topology and Mal\u2032cev products. I","volume":"1","author":"Henckell, Karsten","year":"1991","journal-title":"Internat. J. Algebra Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0218-1967","issn-type":"print"},{"key":"21","series-title":"Oxford Science Publications","isbn-type":"print","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198535775.001.0001","volume-title":"Techniques of semigroup theory","author":"Higgins, Peter M.","year":"1992","ISBN":"https:\/\/id.crossref.org\/isbn\/0198535775"},{"key":"22","series-title":"London Mathematical Society Monographs. New Series","isbn-type":"print","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198511946.001.0001","volume-title":"Fundamentals of semigroup theory","volume":"12","author":"Howie, John M.","year":"1995","ISBN":"https:\/\/id.crossref.org\/isbn\/0198511949"},{"key":"23","doi-asserted-by":"publisher","first-page":"450","DOI":"10.2307\/1994127","article-title":"Algebraic theory of machines. I. Prime decomposition theorem for finite semigroups and machines","volume":"116","author":"Krohn, Kenneth","year":"1965","journal-title":"Trans. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9947","issn-type":"print"},{"key":"24","doi-asserted-by":"publisher","first-page":"128","DOI":"10.2307\/1970558","article-title":"Complexity of finite semigroups","volume":"88","author":"Krohn, Kenneth","year":"1968","journal-title":"Ann. of Math. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0003-486X","issn-type":"print"},{"key":"25","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1142\/9789812816689","volume-title":"Inverse semigroups","author":"Lawson, Mark V.","year":"1998","ISBN":"https:\/\/id.crossref.org\/isbn\/9810233167"},{"issue":"1","key":"26","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1016\/0022-4049(89)90052-2","article-title":"\ud835\udc38-unitary inverse monoids and the Cayley graph of a group presentation","volume":"58","author":"Margolis, Stuart W.","year":"1989","journal-title":"J. Pure Appl. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0022-4049","issn-type":"print"},{"issue":"1","key":"27","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1142\/S021819679300007X","article-title":"Free inverse monoids and graph immersions","volume":"3","author":"Margolis, Stuart W.","year":"1993","journal-title":"Internat. J. Algebra Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0218-1967","issn-type":"print"},{"key":"28","unstructured":"S. W. Margolis and J.-E. Pin, Varieties of finite monoids and topology for the free monoid, pp 113\u2013130 in: Proceedings of the 1984 Marquette Conference on Semigroups, K. Byleen, P. Jones and F. Pastijn, eds., Marquette University, Milwaukee, 1984."},{"issue":"4","key":"29","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1142\/S0218196701000498","article-title":"Closed subgroups in pro-\ud835\udc15 topologies and the extension problem for inverse automata","volume":"11","author":"Margolis, S.","year":"2001","journal-title":"Internat. J. Algebra Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0218-1967","issn-type":"print"},{"key":"30","doi-asserted-by":"publisher","first-page":"227","DOI":"10.2307\/1996831","article-title":"Groups, semilattices and inverse semigroups. I, II","volume":"192","author":"McAlister, D. B.","year":"1974","journal-title":"Trans. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9947","issn-type":"print"},{"key":"31","unstructured":"J. McCammond and J. Rhodes, Geometric semigroup theory, Internat. J. Algebra Comput. (to appear)."},{"key":"32","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1112\/plms\/s3-29.3.385","article-title":"Free inverse semigroups","volume":"29","author":"Munn, W. D.","year":"1974","journal-title":"Proc. London Math. Soc. (3)","ISSN":"https:\/\/id.crossref.org\/issn\/0024-6115","issn-type":"print"},{"key":"33","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-88599-0","volume-title":"Varieties of groups","author":"Neumann, Hanna","year":"1967"},{"issue":"1","key":"34","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1016\/0022-4049(92)90019-C","article-title":"Separability properties of free groups and surface groups","volume":"78","author":"Niblo, G. A.","year":"1992","journal-title":"J. Pure Appl. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0022-4049","issn-type":"print"},{"key":"35","first-page":"33","article-title":"\ud835\udc35\ud835\udc3a=\ud835\udc43\ud835\udc3a: a success story","author":"Pin, Jean-Eric","year":"1995"},{"issue":"4","key":"36","doi-asserted-by":"publisher","first-page":"356","DOI":"10.1112\/blms\/23.4.356","article-title":"A conjecture on the Hall topology for the free group","volume":"23","author":"Pin, Jean-Eric","year":"1991","journal-title":"Bull. London Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0024-6093","issn-type":"print"},{"issue":"3-4","key":"37","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1142\/S021819679900028X","article-title":"Pointlike sets, hyperdecidability and the identity problem for finite semigroups","volume":"9","author":"Rhode, John","year":"1999","journal-title":"Internat. J. Algebra Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0218-1967","issn-type":"print"},{"issue":"6","key":"38","doi-asserted-by":"publisher","first-page":"627","DOI":"10.1142\/S0218196701000784","article-title":"Profinite semigroups, varieties, expansions and the structure of relatively free profinite semigroups","volume":"11","author":"Rhodes, John","year":"2001","journal-title":"Internat. J. Algebra Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0218-1967","issn-type":"print"},{"issue":"1","key":"39","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1112\/blms\/25.1.37","article-title":"On the profinite topology on a free group","volume":"25","author":"Ribes, Luis","year":"1993","journal-title":"Bull. London Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0024-6093","issn-type":"print"},{"issue":"3","key":"40","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1142\/S021819679400004X","article-title":"The pro-\ud835\udc5d topology of a free group and algorithmic problems in semigroups","volume":"4","author":"Ribes, Luis","year":"1994","journal-title":"Internat. J. Algebra Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0218-1967","issn-type":"print"},{"key":"41","first-page":"75","article-title":"Pro-\ud835\udc5d trees and applications","author":"Ribes, Luis","year":"2000"},{"key":"42","series-title":"Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics]","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-04097-3","volume-title":"Profinite groups","volume":"40","author":"Ribes, Luis","year":"2000","ISBN":"https:\/\/id.crossref.org\/isbn\/3540669868"},{"key":"43","unstructured":"L. Ribes and P. A. Zalesski\u012d, Profinite Trees, Springer (to appear)."},{"key":"44","isbn-type":"print","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-61856-7","volume-title":"Trees","author":"Serre, Jean-Pierre","year":"1980","ISBN":"https:\/\/id.crossref.org\/isbn\/3540101039"},{"issue":"3","key":"45","doi-asserted-by":"publisher","first-page":"551","DOI":"10.1007\/BF02095993","article-title":"Topology of finite graphs","volume":"71","author":"Stallings, John R.","year":"1983","journal-title":"Invent. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0020-9910","issn-type":"print"},{"issue":"2","key":"46","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1142\/S0218196798000119","article-title":"On pointlike sets and joins of pseudovarieties","volume":"8","author":"Steinberg, Benjamin","year":"1998","journal-title":"Internat. J. Algebra Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0218-1967","issn-type":"print"},{"issue":"1","key":"47","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/PL00020979","article-title":"On algorithmic problems for joins of pseudovarieties","volume":"62","author":"Steinberg, Benjamin","year":"2001","journal-title":"Semigroup Forum","ISSN":"https:\/\/id.crossref.org\/issn\/0037-1912","issn-type":"print"},{"issue":"1","key":"48","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1142\/S0218196701000462","article-title":"Inevitable graphs and profinite topologies: some solutions to algorithmic problems in monoid and automata theory, stemming from group theory","volume":"11","author":"Steinberg, Benjamin","year":"2001","journal-title":"Internat. J. Algebra Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0218-1967","issn-type":"print"},{"issue":"3","key":"49","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1007\/s002330010051","article-title":"A delay theorem for pointlikes","volume":"63","author":"Steinberg, Benjamin","year":"2001","journal-title":"Semigroup Forum","ISSN":"https:\/\/id.crossref.org\/issn\/0037-1912","issn-type":"print"},{"issue":"9","key":"50","doi-asserted-by":"publisher","first-page":"3409","DOI":"10.1090\/S0002-9947-01-02774-X","article-title":"Finite state automata: a geometric approach","volume":"353","author":"Steinberg, Benjamin","year":"2001","journal-title":"Trans. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9947","issn-type":"print"},{"issue":"5","key":"51","doi-asserted-by":"publisher","first-page":"603","DOI":"10.1142\/S0218196700000285","article-title":"Polynomial closure and topology","volume":"10","author":"Steinberg, Benjamin","year":"2000","journal-title":"Internat. J. Algebra Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0218-1967","issn-type":"print"},{"issue":"2-3","key":"52","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1016\/S0022-4049(01)00030-5","article-title":"Inverse automata and profinite topologies on a free group","volume":"167","author":"Steinberg, Benjamin","year":"2002","journal-title":"J. Pure Appl. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0022-4049","issn-type":"print"},{"key":"53","first-page":"181","article-title":"\ud835\udc43\ud835\udc3a=\ud835\udc35\ud835\udc3a: redux","author":"Steinberg, B.","year":"2000"},{"key":"54","doi-asserted-by":"crossref","unstructured":"B. Steinberg, The uniform word problem for groups and finite Rees quotients of \ud835\udc38-unitary inverse semigroups, J. Algebra 266 (2003), 1\u201313.","DOI":"10.1016\/S0021-8693(03)00312-0"},{"issue":"1","key":"55","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1016\/0022-4049(90)90057-O","article-title":"Presentations of inverse monoids","volume":"63","author":"Stephen, J. B.","year":"1990","journal-title":"J. Pure Appl. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0022-4049","issn-type":"print"},{"issue":"1-2","key":"56","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1016\/0022-4049(87)90108-3","article-title":"Categories as algebra: an essential ingredient in the theory of monoids","volume":"48","author":"Tilson, Bret","year":"1987","journal-title":"J. Pure Appl. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0022-4049","issn-type":"print"},{"key":"57","first-page":"289","article-title":"Computing closures of finitely generated subgroups of the free group","author":"Weil, Pascal","year":"2000"},{"issue":"2","key":"58","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1007\/BF00971377","article-title":"Geometric characterization of free constructions of profinite groups","volume":"30","author":"Zalesski\u012d, P. A.","year":"1989","journal-title":"Sibirsk. Mat. Zh.","ISSN":"https:\/\/id.crossref.org\/issn\/0037-4474","issn-type":"print"},{"issue":"4","key":"59","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1070\/SM1989v063n02ABEH003282","article-title":"Subgroups of profinite groups acting on trees","volume":"135(177)","author":"Zalesski\u012d, P. A.","year":"1988","journal-title":"Mat. Sb. (N.S.)","ISSN":"https:\/\/id.crossref.org\/issn\/0368-8666","issn-type":"print"}],"container-title":["Transactions of the American Mathematical Society"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/tran\/2004-356-02\/S0002-9947-03-03358-0\/S0002-9947-03-03358-0.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/tran\/2004-356-02\/S0002-9947-03-03358-0\/S0002-9947-03-03358-0.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,11]],"date-time":"2024-01-11T01:05:55Z","timestamp":1704935155000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/tran\/2004-356-02\/S0002-9947-03-03358-0\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,8,21]]},"references-count":59,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2004,2]]}},"alternative-id":["S0002-9947-03-03358-0"],"URL":"https:\/\/doi.org\/10.1090\/s0002-9947-03-03358-0","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["0002-9947","1088-6850"],"issn-type":[{"value":"0002-9947","type":"print"},{"value":"1088-6850","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,8,21]]}}}