{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,12,2]],"date-time":"2023-12-02T22:45:21Z","timestamp":1701557121425},"reference-count":14,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,12,13]],"date-time":"2022-12-13T00:00:00Z","timestamp":1670889600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,12,13]],"date-time":"2022-12-13T00:00:00Z","timestamp":1670889600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Period Math Hung"],"published-print":{"date-parts":[[2023,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We build on the description of left congruences on an inverse semigroup in terms of the kernel and trace due to Petrich and Rankin. The notion of an inverse kernel for a left congruence is developed. Various properties of the trace and inverse kernel are discussed, in particular that the inverse kernel is a full inverse subsemigroup and that both the trace and inverse kernel maps are onto<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\cap $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mo>\u2229<\/mml:mo><\/mml:math><\/jats:alternatives><\/jats:inline-formula>-homomorphisms. It is shown that a left congruence is determined by its trace and inverse kernel, and the lattice of left congruences is identified as a subset of the direct product of the lattice of congruences on the idempotents and the lattice of full inverse subsemigroups. We demonstrate that every finitely generated left congruence is the join of a finitely generated trace minimal left congruence and a finitely generated idempotent separating left congruence. Characterisations are given of inverse semigroups that are left Noetherian, or are such that Rees left congruences are finitely generated.<\/jats:p>","DOI":"10.1007\/s10998-022-00497-z","type":"journal-article","created":{"date-parts":[[2022,12,13]],"date-time":"2022-12-13T16:10:49Z","timestamp":1670947849000},"page":"1-26","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The lattice of one-sided congruences on an inverse semigroup"],"prefix":"10.1007","volume":"87","author":[{"given":"Matthew D. G. K.","family":"Brookes","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,12,13]]},"reference":[{"issue":"4","key":"497_CR1","doi-asserted-by":"publisher","first-page":"689","DOI":"10.1007\/s00605-019-01274-w","volume":"190","author":"Y Dandan","year":"2019","unstructured":"Y. Dandan, V. Gould, T. Quinn-Gregson, R.-E. Zenab, Semigroups with finitely generated universal left congruence. Monatshefte f\u00fcr Math. 190(4), 689\u2013724 (2019)","journal-title":"Monatshefte f\u00fcr Math."},{"issue":"01","key":"497_CR2","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1142\/S0218196705002098","volume":"15","author":"L Descal\u00e7o","year":"2005","unstructured":"L. Descal\u00e7o, N. Ru\u0161kuc, Subsemigroups of the bicyclic monoid. Int. J. Algebra Comput. 15(01), 37\u201357 (2005)","journal-title":"Int. J. Algebra Comput."},{"issue":"1","key":"497_CR3","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1007\/BF02573180","volume":"33","author":"G Duchamp","year":"1986","unstructured":"G. Duchamp, \u00c9tude du treillis des congruences \u00e0 droite sur le mono\u00efde bicyclique. Semigroup Forum 33(1), 31\u201346 (1986)","journal-title":"Semigroup Forum"},{"issue":"1","key":"497_CR4","doi-asserted-by":"publisher","first-page":"141","DOI":"10.2140\/pjm.1975.57.141","volume":"57","author":"DG Green","year":"1975","unstructured":"D.G. Green, The lattice of congruences on an inverse semigroup. Pacific J. Math. 57(1), 141\u2013152 (1975)","journal-title":"Pacific J. Math."},{"key":"497_CR5","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198511946.001.0001","volume-title":"Fundamentals of Semigroup Theory","author":"JM Howie","year":"1995","unstructured":"J.M. Howie, Fundamentals of Semigroup Theory (Clarendon, Oxford, 1995)"},{"issue":"3","key":"497_CR6","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1112\/jlms\/s2-17.3.457","volume":"2","author":"PR Jones","year":"1978","unstructured":"P.R. Jones, Distributive inverse semigroups. J. Lond. Math. Soc. 2(3), 457\u2013466 (1978)","journal-title":"J. Lond. Math. 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