TY - JOUR AU - Shou-Feng Wang PY - 2016/11/25 Y2 - 2024/03/28 TI - A construction of regular semigroups with quasiideal regular *-transversals JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 68 IS - 11 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/1941 AB - 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 constructionof regular semigroups with quasiideal regular $\ast$ -transversals based on the use of fundamental regular semigroups and regular$\ast$ -semigroups. ER -