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- Publisher
- Springer Journals
- Copyright
- Copyright © 2014 by Malaysian Mathematical Sciences Society and Universiti Sains Malaysia
- Subject
- Mathematics; Mathematics, general; Applications of Mathematics
- ISSN
- 0126-6705
- eISSN
- 2180-4206
- DOI
- 10.1007/s40840-014-0070-4
- Publisher site
- See Article on Publisher Site
Abstract
Let $$S$$ S be a semigroup and “ $$*$$ ∗ ” a unary operation on $$S$$ S which satisfies the following identities $$\begin{aligned} xx^*x=x, x^*x x^*=x^*, x^{***}=x^*, (xy^*)^*=y^{**}x^*, (x^*y)^*=y^*x^{**}. \end{aligned}$$ x x ∗ x = x , x ∗ x x ∗ = x ∗ , x ∗ ∗ ∗ = x ∗ , ( x y ∗ ) ∗ = y ∗ ∗ x ∗ , ( x ∗ y ) ∗ = y ∗ x ∗ ∗ . Then, $$S^*=\{x^*|x\in S\}$$ S ∗ = { x ∗ | x ∈ S } is called a regular $$*$$ ∗ -transversal of $$S$$ S in the literatures. Following Munn and Hall’s idea, in this paper we construct fundamental regular semigroups with quasi-ideal regular $$*$$ ∗ -transversals by which fundamental representations of regular semigroups with quasi-ideal regular $$*$$ ∗ -transversals are obtained.
Journal
Bulletin of the Malaysian Mathematical Sciences Society – Springer Journals
Published: Dec 3, 2014