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A NEW CONSTRUCTION FOR REGULAR SEMIGROUPS WITH QUASI-IDEAL ORTHODOX TRANSVERSALS

Part of: Semigroups

Published online by Cambridge University Press:  01 April 2009

XIANGJUN KONG  and
XIANZHONG ZHAO
XIANGJUN KONG*
Affiliation:
School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, People’s Republic of China
XIANZHONG ZHAO
Affiliation:
Department of Mathematics, Northwest University, Xi’an, Shaanxi 710069, People’s Republic of China
*
✉For correspondence; e-mail: xiangjunkong97@163.com
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Abstract

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In any regular semigroup with an orthodox transversal, we define two sets R and L using Green’s relations and give necessary and sufficient conditions for them to be subsemigroups. By using R and L, some equivalent conditions for an orthodox transversal to be a quasi-ideal are obtained. Finally, we give a structure theorem for regular semigroups with quasi-ideal orthodox transversals by two orthodox semigroups R and L.

Keywords

regular semigroupinverse transversalorthodox transversalquasi-ideal

MSC classification

Secondary: 20M10: General structure theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 86 , Issue 2 , April 2009 , pp. 177 - 187
Copyright
Copyright © Australian Mathematical Society 2009

References

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