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dc.contributor.authorEast, James
dc.contributor.authorRuskuc, Nik
dc.date.accessioned2020-06-19T15:30:01Z
dc.date.available2020-06-19T15:30:01Z
dc.date.issued2020-05-25
dc.identifier.citationEast , J & Ruskuc , N 2020 , ' Congruence lattices of ideals in categories and (partial) semigroups ' , Memoirs of the American Mathematical Society , vol. 0 , pp. 2-108 . < https://arxiv.org/abs/2001.01909 >en
dc.identifier.issn0065-9266
dc.identifier.otherPURE: 268137641
dc.identifier.otherPURE UUID: d067b6e4-de02-417f-bf2c-10124ee5aa01
dc.identifier.urihttp://hdl.handle.net/10023/20107
dc.descriptionFunding: UK EPSRC grant EP/S020616/1 (NR).en
dc.description.abstractThis paper presents a unified framework for determining the congruences on a number of monoids and categories of transformations, diagrams, matrices and braids, and on all their ideals. The key theoretical advances present an iterative process of stacking certain normal subgroup lattices on top of each other to successively build congruence lattices ofa chain of ideals. This is applied to several specific categories of: transformations; order/orientation preserving/reversing transformations; partitions; planar/annular partitions; Brauer, Temperley–Lieb and Jones partitions; linear and projective linear transformations; and partial braids. Special considerations are needed for certain small ideals, and technically more intricate theoretical underpinnings for the linear and partial braid categories.
dc.language.isoeng
dc.relation.ispartofMemoirs of the American Mathematical Societyen
dc.rightsCopyright © 2020 American Mathematical Society. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://www.ams.org/publications/ebooks/memoirsen
dc.subjectCategoriesen
dc.subjectSemigroupsen
dc.subjectCongruencesen
dc.subjectH-congruencesen
dc.subjectLatticsen
dc.subjectIdealsen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subjectBDCen
dc.subjectR2Cen
dc.subject.lccQAen
dc.titleCongruence lattices of ideals in categories and (partial) semigroupsen
dc.typeJournal articleen
dc.description.versionPostprinten
dc.contributor.institutionUniversity of St Andrews.Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews.Centre for Interdisciplinary Research in Computational Algebraen
dc.description.statusPeer revieweden
dc.identifier.urlhttps://www.ams.org/cgi-bin/mstrack/accepted_papers/memoen
dc.identifier.urlhttps://arxiv.org/abs/2001.01909en


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