Various regularities for semigroups of transformations on a finite set determined by a zig-zag order-Reference-Cited by-同舟云学术

Various regularities for semigroups of transformations on a finite set determined by a zig-zag order

Published:2022-03-15 Issue:04 Volume:15 Page:
ISSN:1793-5571
Container-title:Asian-European Journal of Mathematics
language:en
Short-container-title:Asian-European J. Math.

Author:

Prinyasart Thanakorn¹,Srithus Ratana¹^ORCID,Nuntharatkul Jirapa¹

Affiliation:

1. Department of Mathematics, Faculty of Science, Silpakorn University, Sanam Chan Palace Campus, Nakhon Pathom 73000, Thailand

Abstract

Consider a finite ordered set [Formula: see text] with a zig-zag order. In this paper, we consider the semigroup [Formula: see text] of all compressing-preserving transformations on [Formula: see text]. Necessary and sufficient conditions for [Formula: see text] to be regular and coregular are given. Regular and coregular elements in [Formula: see text] are completely described. For a subsemigroup [Formula: see text] of the transformation semigroup [Formula: see text], we obtain that left regular and right regular elements in [Formula: see text] are identical. A characterization of left [right] regular elements in [Formula: see text] is given. We classify all left [right] regular semigroups [Formula: see text].

Funder

Faculty of Science, Silpakorn University

Publisher

World Scientific Pub Co Pte Ltd

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793557122502084

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