{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T22:00:07Z","timestamp":1747173607320,"version":"3.40.5"},"reference-count":10,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2023,12,13]],"date-time":"2023-12-13T00:00:00Z","timestamp":1702425600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["J. Aust. Math. Soc."],"published-print":{"date-parts":[[2024,6]]},"abstract":"Abstract<\/jats:title>The complex algebra of an inverse semigroup with finitely many idempotents in each \n$\\mathcal D$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-class is stably finite by a result of Munn. This can be proved fairly easily using \n$C^{*}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-algebras for inverse semigroups satisfying this condition that have a Hausdorff universal groupoid, or more generally for direct limits of inverse semigroups satisfying this condition and having Hausdorff universal groupoids. It is not difficult to see that a finitely presented inverse semigroup with a non-Hausdorff universal groupoid cannot be a direct limit of inverse semigroups with Hausdorff universal groupoids. We construct here countably many nonisomorphic finitely presented inverse semigroups with finitely many idempotents in each \n$\\mathcal D$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-class and non-Hausdorff universal groupoids. At this time, there is not a clear \n$C^{*}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-algebraic technique to prove these inverse semigroups have stably finite complex algebras.<\/jats:p>","DOI":"10.1017\/s1446788723000198","type":"journal-article","created":{"date-parts":[[2023,12,13]],"date-time":"2023-12-13T10:50:06Z","timestamp":1702464606000},"page":"384-398","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["FINITELY PRESENTED INVERSE SEMIGROUPS WITH FINITELY MANY IDEMPOTENTS IN EACH -CLASS AND NON-HAUSDORFF UNIVERSAL GROUPOIDS"],"prefix":"10.1017","volume":"116","author":[{"given":"PEDRO V.","family":"SILVA","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3636-4255","authenticated-orcid":false,"given":"BENJAMIN","family":"STEINBERG","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2023,12,13]]},"reference":[{"key":"S1446788723000198_r5","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1774-9","volume-title":"Groupoids, Inverse Semigroups, and their Operator Algebras","author":"Paterson","year":"1999"},{"key":"S1446788723000198_r3","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1112\/plms\/s3-29.3.385","article-title":"Free inverse semigroups","volume":"29","author":"Munn","year":"1974","journal-title":"Proc. Lond. Math. Soc. (3)"},{"key":"S1446788723000198_r2","doi-asserted-by":"crossref","DOI":"10.1142\/3645","volume-title":"Inverse Semigroups: The Theory of Partial Symmetries","author":"Lawson","year":"1998"},{"key":"S1446788723000198_r4","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1017\/S0013091500023087","article-title":"Direct finiteness of certain monoid algebras. I","volume":"39","author":"Munn","year":"1996","journal-title":"Proc. Edinb. Math. Soc. (2)"},{"key":"S1446788723000198_r6","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139195218","volume-title":"Elements of Automata Theory","author":"Sakarovitch","year":"2009"},{"key":"S1446788723000198_r7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0002-9939-1973-0310093-1","article-title":"Free inverse semigroups","volume":"38","author":"Scheiblich","year":"1973","journal-title":"Proc. Amer. Math. Soc."},{"key":"S1446788723000198_r9","unstructured":"[9] Steinberg, B. , \u2018Stable finiteness of ample groupoid algebras, traces and applications\u2019, Preprint, 2022, arXiv:2207.11194."},{"key":"S1446788723000198_r8","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1016\/j.aim.2009.09.001","article-title":"A groupoid approach to discrete inverse semigroup algebras","volume":"223","author":"Steinberg","year":"2010","journal-title":"Adv. Math."},{"volume-title":"Handbook of Automata Theory","year":"2021","author":"Bartholdi","key":"S1446788723000198_r1"},{"key":"S1446788723000198_r10","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/0022-4049(90)90057-O","article-title":"Presentations of inverse monoids","volume":"63","author":"Stephen","year":"1990","journal-title":"J. Pure Appl. Algebra"}],"container-title":["Journal of the Australian Mathematical Society"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1446788723000198","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,13]],"date-time":"2024-05-13T13:27:02Z","timestamp":1715606822000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1446788723000198\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,13]]},"references-count":10,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,6]]}},"alternative-id":["S1446788723000198"],"URL":"https:\/\/doi.org\/10.1017\/s1446788723000198","relation":{},"ISSN":["1446-7887","1446-8107"],"issn-type":[{"type":"print","value":"1446-7887"},{"type":"electronic","value":"1446-8107"}],"subject":[],"published":{"date-parts":[[2023,12,13]]},"assertion":[{"value":"\u00a9 The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}