Please use this identifier to cite or link to this item:
https://open.uns.ac.rs/handle/123456789/19671
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Ying-Ying Feng | - |
dc.contributor.author | Asawer Al-Aadhami | - |
dc.contributor.author | Dolinka Igor | - |
dc.contributor.author | East James | - |
dc.contributor.author | Gould Victoria | - |
dc.date.accessioned | 2020-12-13T13:58:11Z | - |
dc.date.available | 2020-12-13T13:58:11Z | - |
dc.date.issued | 2019 | - |
dc.identifier.issn | 0022-4049 | - |
dc.identifier.uri | https://open.uns.ac.rs/handle/123456789/19671 | - |
dc.description.abstract | © 2019 Elsevier B.V. For a monoid M and a subsemigroup S of the full transformation semigroup Tn, the wreath product M≀S is defined to be the semidirect product Mn⋊S, with the coordinatewise action of S on Mn. The full wreath product M≀Tn is isomorphic to the endomorphism monoid of the free M-act on n generators. Here we are particularly interested in the case that S=Singn is the singular part of Tn, consisting of all non-invertible transformations. Our main results are presentations for M≀Singn in terms of certain natural generating sets, and we prove these via general results on semidirect products and wreath products. We re-prove a classical result of Bulman-Fleming that M≀Singn is idempotent-generated if and only if the set M/L of L-classes of M forms a chain under the usual ordering of L-classes, and we give a presentation for M≀Singn in terms of idempotent generators for such a monoid M. Among other results, we also give estimates for the minimal size of a generating set for M≀Singn, as well as exact values in some cases (including the case that M is finite and M/L is a chain, in which case we also calculate the minimal size of an idempotent generating set). As an application of our results, we obtain a presentation (with idempotent generators) for the idempotent-generated subsemigroup of the endomorphism monoid of a uniform partition of a finite set. | - |
dc.language.iso | en | - |
dc.relation.ispartof | Journal of Pure and Applied Algebra | - |
dc.source | CRIS UNS | - |
dc.source.uri | http://cris.uns.ac.rs | - |
dc.title | Presentations for singular wreath products | - |
dc.type | Journal/Magazine Article | - |
dc.identifier.doi | 10.1016/j.jpaa.2019.03.013 | - |
dc.identifier.scopus | 2-s2.0-85063073227 | - |
dc.identifier.url | https://www.cris.uns.ac.rs/record.jsf?recordId=110818&source=BEOPEN&language=en | - |
dc.identifier.url | https://api.elsevier.com/content/abstract/scopus_id/85063073227 | - |
dc.relation.lastpage | 5146 | - |
dc.relation.firstpage | 5106 | - |
dc.relation.issue | 12 | - |
dc.relation.volume | 223 | - |
dc.identifier.externalcrisreference | (BISIS)110818 | - |
item.grantfulltext | none | - |
item.fulltext | No Fulltext | - |
crisitem.author.dept | Prirodno-matematički fakultet, Departman za matematiku i informatiku | - |
crisitem.author.orcid | 0000-0002-8644-0626 | - |
crisitem.author.parentorg | Prirodno-matematički fakultet | - |
Appears in Collections: | PMF Publikacije/Publications |
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