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Semigroups with operation-compatible Green’s quasiorders

Juhász, Z and Vernitski, A (2016) 'Semigroups with operation-compatible Green’s quasiorders.' Semigroup Forum, 93 (2). 387 - 402. ISSN 0037-1912

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Abstract

We call a semigroup on which the Green’s quasiorder ≤ (≤ , ≤ ) is operation-compatible, a ≤ -compatible (≤ -compatible, ≤ -compatible) semigroup. We study the classes of ≤ -compatible, ≤ -compatible and ≤ -compatible semigroups, using the smallest operation-compatible quasiorders containing Green’s quasiorders as a tool. We prove a number of results, including the following. The class of ≤ -compatible (≤ -compatible) semigroups is closed under taking homomorphic images. A regular periodic semigroup is ≤ -compatible if and only if it is a semilattice of simple semigroups. Every negatively orderable semigroup can be embedded into a negatively orderable ≤ -compatible semigroup. J L R J L R J L R L R J J

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Jim Jamieson
Date Deposited: 10 Mar 2016 19:29
Last Modified: 07 Apr 2021 10:16
URI: http://repository.essex.ac.uk/id/eprint/16244

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