Regular semigroups with weakly simplistic orthodox transversals
Weakly simplistic orthodox transversals are introduced in this paper and some characterizations associated with them are obtained. An example is given to demonstrate that weakly simplistic orthodox transversals are proper generalisations of left simplistic orthodox transversals. The related results of Blyth and Almeida Santos on left simplistic inverse transversals obtained in 1996 and Kong and Luo on left simplistic orthodox transversals obtained in 2011 are generalised and amplified. A structure theorem of regular semigroups with weakly simplistic orthodox transversals is also established.
KeywordsRegular semigroup Orthodox semigroup Weakly simplistic orthodox transversal
The author would like to express his sincere thanks to M.Jackson and the referee for their valuable suggestions and corrections, which much improved this paper. The author is a postdoctoral researcher of the Postdoctoral Station of Qufu Normal University. The research is partially supported by NSF of Shandong Province (ZR2016AM02), the NSFC (11471186), A Project of Shandong Province Higher Educational Science and Technology Program (J18KA248) and Scientific Research Foundation of Qufu Normal University (xkj201509).