Semilattices of stratified extensions
Semilattices of stratified extensions
Grillet (Semigroup Forum 50:25–36, 1995) introduced the concept of stratified semigroups as a kind of generalisation of finite nilsemigroups. We extend Grillet’s ideas by introducing the notion of the base of a semigroup and show that a semigroup is stratified if and only if its base is either empty or consists of only the zero element. The general structure of semigroups with non-trivial bases is studied and we show that these can be described in terms of ideal extensions of semigroups by stratified semigroups. We consider certain types of group-bound semigroups and also ideal extensions of Clifford semigroups, and show how to describe them as semilattices of ideal extensions by stratified semigroups and provide a number of interesting examples.
Semigroup, stratified, extension, semilattice, group-bound, Clifford semigroup, Extension, Group-bound, Semilattice, Stratified, Semigroup, Clifford semigroup
Renshaw, Jim
350100c1-f7c7-44d3-acfb-29b94f21731c
Warhurst, William
a78b4743-0ddd-49de-9a35-c95c0cf11e7e
24 June 2024
Renshaw, Jim
350100c1-f7c7-44d3-acfb-29b94f21731c
Warhurst, William
a78b4743-0ddd-49de-9a35-c95c0cf11e7e
Abstract
Grillet (Semigroup Forum 50:25–36, 1995) introduced the concept of stratified semigroups as a kind of generalisation of finite nilsemigroups. We extend Grillet’s ideas by introducing the notion of the base of a semigroup and show that a semigroup is stratified if and only if its base is either empty or consists of only the zero element. The general structure of semigroups with non-trivial bases is studied and we show that these can be described in terms of ideal extensions of semigroups by stratified semigroups. We consider certain types of group-bound semigroups and also ideal extensions of Clifford semigroups, and show how to describe them as semilattices of ideal extensions by stratified semigroups and provide a number of interesting examples.
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stratified_semigroups
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s00233-024-10447-5 (1)
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Accepted/In Press date: 14 June 2024
Published date: 24 June 2024
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© The Author(s) 2024.
Keywords:
Semigroup, stratified, extension, semilattice, group-bound, Clifford semigroup, Extension, Group-bound, Semilattice, Stratified, Semigroup, Clifford semigroup
Identifiers
Local EPrints ID: 491315
URI: http://eprints.soton.ac.uk/id/eprint/491315
ISSN: 0037-1912
PURE UUID: cfa28e87-eb26-42d6-bdc2-ef1e6a814ba6
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Date deposited: 19 Jun 2024 16:51
Last modified: 12 Jul 2024 02:03
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Author:
William Warhurst
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