Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2012; 27(4): 689-699

Printed December 1, 2012

https://doi.org/10.4134/CKMS.2012.27.4.689

Copyright © The Korean Mathematical Society.

$E$-inversive $\ast$-semigroups

Shoufeng Wang and Yinghui Li

Yunnan Normal University, Kunming College

Abstract

$(S,\ast)$ is a semigroup $S$ equipped with a unary operation "$\ast$". This work is devoted to a class of unary semigroups, namely $E$-inversive $\ast$-semigroups. A unary semigroup $(S,\ast)$ is called an $E$-inversive $\ast$-semigroup if the following identities hold: $$x^\ast x x^\ast=x^\ast, {(x^\ast)}^\ast=x x^\ast x, (xy)^\ast=y^\ast x^\ast.$$ In this paper, $E$-inversive $\ast$-semigroups are characterized by several methods. Furthermore, congruences on these semigroups are also studied.

Keywords: $E$-inversive $\ast$-semigroups, $\bf wp$-systems, congruences

MSC numbers: 20M10