{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T07:08:08Z","timestamp":1769584088982,"version":"3.49.0"},"reference-count":13,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2007,6]]},"abstract":"<jats:p> Let G be a group, R be a ring and A be an RG-module. We say that A is an Artinian-finitary module overRG if for every element g \u2208 G, the factor-module A\/C<jats:sub>A<\/jats:sub>(g) is an Artinian R-module. The study of these modules was initiated by Wehrfritz. If D is a Dedekind domain and U is an Artinian D-module, then we can associate with U some numerical invariants. If V is the maximal divisible submodule of U, then V is a direct sum of finitely many indecomposable submodules. The number b<jats:sub>d<\/jats:sub>(U) of these direct summands is an invariant of U. The composition length b<jats:sub>F<\/jats:sub>(U\/V) of U\/V is another invariant of U. We consider the following special case of Artinian-finitary modules. Let D be a Dedekind domain and G be a group. The DG-module A is said to be bounded Artinian-finitary, if A is Artinian-finitary and there are the numbers b<jats:sub>F<\/jats:sub>(A) = b, b<jats:sub>d<\/jats:sub>(A) = d \u2208 \u2115 and a finite subset b<jats:sub>\u03c3<\/jats:sub>(A) = \u03c4 Spec (D) such that l<jats:sub>F<\/jats:sub>(A\/C<jats:sub>A<\/jats:sub>(g)) \u2264 b, l<jats:sub>d<\/jats:sub>(A\/C<jats:sub>A<\/jats:sub>(g)) \u2264 d and Ass <jats:sub>D<\/jats:sub>(A\/C<jats:sub>A<\/jats:sub>(g)) \u2286 \u03c4 for every element g \u2208 G. In the article, the bounded Artinian-finitary modules under some natural restriction are studied. <\/jats:p>","DOI":"10.1142\/s021819670700386x","type":"journal-article","created":{"date-parts":[[2007,7,5]],"date-time":"2007-07-05T05:38:16Z","timestamp":1183613896000},"page":"881-893","source":"Crossref","is-referenced-by-count":4,"title":["ON BOUNDED ARTINIAN-FINITARY MODULES"],"prefix":"10.1142","volume":"17","author":[{"given":"L. A.","family":"KURDACHENKO","sequence":"first","affiliation":[{"name":"Department of Mathematics, Dnipropetrovsk National University, Vulycya Naykova 13, Dnipropetrovsk 49050, Ukraine"}]},{"given":"I. YA.","family":"SUBBOTIN","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Natural Sciences, National University, 5245 Pacific Concourse Drive, Los Angeles, CA 90045-6904, USA"}]},{"given":"V. A.","family":"CHUPORDYA","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Dnipropetrovsk National University, Vulycya Naykova 13, Dnipropetrovsk 49050, Ukraine"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf2","first-page":"53","volume":"14","author":"Grigorchuk R. I.","journal-title":"Funktsional Anal. i Prilozhen."},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1380-2_4"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1142\/9789812778291"},{"key":"rf6","unstructured":"L. A.\u00a0Kurdachenko, J.\u00a0Otal and I.\u00a0Ya. Subbotin, Artinian Modules Over Group Rings (Birkh\u00e4user, 2006)\u00a0p. 259."},{"key":"rf7","first-page":"351","volume":"22","author":"Maltsev A. I.","journal-title":"Sb. Mat."},{"key":"rf8","first-page":"567","volume":"28","author":"Maltsev A. I.","journal-title":"Sb. Mat."},{"key":"rf9","first-page":"49","author":"Matlis E.","journal-title":"Mem. Amer. Math. Soc."},{"key":"rf10","first-page":"5","volume":"3","author":"Merzlyakov Yu. I.","journal-title":"Algebra Logika"},{"key":"rf11","first-page":"236","volume":"29","author":"Neumann B. H.","journal-title":"J. London Math. Soc."},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-0329-9_5"},{"key":"rf13","series-title":"Queen Mary College Mathematics Notes","volume-title":"Infinite soluble and nilpotent groups","author":"Robinson D. J. S.","year":"1968"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1142\/S0219498802000318"},{"key":"rf15","first-page":"753","volume":"54","author":"Wehrfritz B. A. F.","journal-title":"Ukrainian Math. J."}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021819670700386X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T18:27:52Z","timestamp":1565116072000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021819670700386X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,6]]},"references-count":13,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2007,6]]}},"alternative-id":["10.1142\/S021819670700386X"],"URL":"https:\/\/doi.org\/10.1142\/s021819670700386x","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,6]]}}}