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# A Construction of Regular Semigroups with Quasiideal Regular ∗-Transversals

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Let S be a semigroup and let “∗” be a unary operation on S satisfying the following identities:

$$x{x}^{\ast }x=x,\kern1em {x}^{\ast }x{x}^{\ast }={x}^{\ast },\kern1em {x}^{\ast \ast \ast }={x}^{\ast },\kern1em {\left(x{y}^{\ast}\right)}^{\ast }={y}^{\ast \ast }{x}^{\ast },\kern1em {\left({x}^{\ast }y\right)}^{\ast }={y}^{\ast }{x}^{\ast \ast }.$$

Then S  = {x |x ∈ S} is called a regular ∗-transversal of S in the literature. We propose a method for the construction of regular semigroups with quasiideal regular ∗-transversals based on the use of fundamental regular semigroups and regular ∗-semigroups.

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## Author information

Correspondence to Sh.-F. Wang.

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, No. 11, pp. 1552–1560, November, 2016.

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Wang, S. A Construction of Regular Semigroups with Quasiideal Regular ∗-Transversals. Ukr Math J 68, 1798–1807 (2017). https://doi.org/10.1007/s11253-017-1328-4

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