{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T09:43:54Z","timestamp":1775814234343,"version":"3.50.1"},"reference-count":19,"publisher":"World Scientific Pub Co Pte Lt","issue":"03n04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[1999,6]]},"abstract":"<jats:p> The author proves for each of the operations # equalling *, \u00b0, **, \u25a1 or m, there exist pseudovarieties of finite semigroups [Formula: see text] and [Formula: see text] with decidable membership problems, such that [Formula: see text] has an undecidable membership problem. <\/jats:p><jats:p> In addition, if [Formula: see text] denotes the pseudovariety of all finite aperiodic semigroups, [Formula: see text] denotes the pseudovariety of all finite groups, and [Formula: see text](E) denotes the pseudovariety of all finite aperiodic semigroups satisfying the finite number of equations E, then it is proved that there exists E such that [Formula: see text](E) has an undecidable membership problem. Note [Formula: see text] equals all semigroups of complexity \u22641. <\/jats:p><jats:p> Section\u00a06 is expanded into a joint paper with B. Steinberg, following this paper. <\/jats:p>","DOI":"10.1142\/s0218196799000278","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T07:05:54Z","timestamp":1027753554000},"page":"455-473","source":"Crossref","is-referenced-by-count":26,"title":["UNDECIDABILITY, AUTOMATA, AND PSEUDOVARITIES OF FINITE SEMIGROUPS"],"prefix":"10.1142","volume":"09","author":[{"given":"JOHN","family":"RHODES","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of California, Berkeley, California\u00a094720-3840, USA"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.2307\/2275184"},{"key":"p_5","first-page":"128","volume":"1","author":"Ash C. J.","year":"1991","journal-title":"Int. J. Algebra Comp."},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(94)00063-O"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(84)90092-6"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.2307\/2274101"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(88)90042-4"},{"key":"p_13","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196791000298"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.1007\/BF02572755"},{"key":"p_15","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196795000227"},{"key":"p_16","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1965-0188316-1"},{"key":"p_17","first-page":"5","volume":"1","author":"Krohn K.","journal-title":"Chaps."},{"key":"p_19","first-page":"663","volume":"3","author":"Murskii V. L.","year":"1968","journal-title":"Matematicheskie Zametski"},{"key":"p_21","doi-asserted-by":"publisher","DOI":"10.2307\/2267170"},{"key":"p_22","doi-asserted-by":"publisher","DOI":"10.1007\/BF02483902"},{"key":"p_24","first-page":"169","author":"Rhodes J.","year":"1987","journal-title":"Dordrecht"},{"key":"p_26","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(89)90139-4"},{"key":"p_28","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(89)90138-2"},{"key":"p_32","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196798000119"},{"key":"p_33","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(87)90108-3"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196799000278","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T17:56:08Z","timestamp":1565114168000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196799000278"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,6]]},"references-count":19,"journal-issue":{"issue":"03n04","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[1999,6]]}},"alternative-id":["10.1142\/S0218196799000278"],"URL":"https:\/\/doi.org\/10.1142\/s0218196799000278","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,6]]}}}