A construction of regular semigroups with quasiideal regular *-transversals

  • Shou-Feng Wang

Abstract

Let $S$ be a semigroup and let “$\ast$ ” be a unary operation on S satisfying the following identities: $$xx^{\ast} x = x, x^{\ast} xx^{\ast} = x^{\ast},\; x^{\ast \ast \ast} = x^{\ast},\; (xy^{\ast} )^{\ast} = y^{\ast \ast} x^{\ast},\; (x^{\ast} y)^{\ast} = y^{\ast} x^{\ast \ast}.$$ Then S\ast = \{ x\ast | x \in S\} is called a regular \ast -transversal of $S$ in the literatures. We propose a method for the construction of regular semigroups with quasiideal regular $\ast$ -transversals based on the use of fundamental regular semigroups and regular $\ast$ -semigroups.
Published
25.11.2016
How to Cite
Wang, S.-F. “A Construction of Regular Semigroups With Quasiideal Regular *-Transversals”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, no. 11, Nov. 2016, pp. 1552-60, http://umj.imath.kiev.ua/index.php/umj/article/view/1941.
Section
Research articles