Abundance and magnifying elements in transformation semigroups that preserve order and equivalence
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Published:2023-12-02
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Volume:
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ISSN:0219-4988
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Container-title:Journal of Algebra and Its Applications
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language:en
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Short-container-title:J. Algebra Appl.
Affiliation:
1. School of Mathematics and Physics, Yancheng Institute of Technology, Yancheng 224051, P. R. China
Abstract
Let [Formula: see text] be a nontrivial equivalence relation on a totally ordered set [Formula: see text] and [Formula: see text] be the semigroup of all transformations of [Formula: see text] that preserve [Formula: see text]. In this paper, we consider a subsemigroup of [Formula: see text] defined by [Formula: see text] and present a necessary and sufficient condition under which the semigroup [Formula: see text] is abundant. Also, we describe all the left and right magnifying elements in [Formula: see text].
Funder
Yancheng Institute of Technology
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Algebra and Number Theory