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Semigroups with operation-compatible Green’s quasiorders

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

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We call a semigroup on which the Green’s quasiorder ≤ J (≤ L, ≤ R) is operation-compatible, a ≤ J-compatible (≤ L-compatible, ≤ R-compatible) semigroup. We study the classes of ≤ J-compatible, ≤ L-compatible and ≤ R-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 ≤ L-compatible (≤ R-compatible) semigroups is closed under taking homomorphic images. A regular periodic semigroup is ≤ J-compatible if and only if it is a semilattice of simple semigroups. Every negatively orderable semigroup can be embedded into a negatively orderable ≤ J-compatible semigroup.

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 10 Mar 2016 19:29
Last Modified: 15 Jan 2022 00:36

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