Biordered Sets of Regular Semigroups with Inverse Transversals1 |
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Authors: | Xilin Tang Limin Wang |
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Institution: | (1) Department of Mathematics, Guangzhou University, Guangzhou, Guangdong, 510405, P.R. China;(2) Department of Mathematics, South China Normal University, Guangzhou, Guangdong, 510405, P.R. China |
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Abstract: | In a regular semigroup S, an inverse subsemigroup S° of S is called an inverse transversal of S if S° contains a unique inverse x° of each element x of S. An inverse transversal S° of S is called a Q-inverse transversal of S if S° is a quasi-ideal of S.If S is a regular semigroup with set of idempotents E then E is a biordered set. T.E. Hall obtained a fundamental regular semigroup TE from the subsemigroup E which is generated by the set of idempotents of a regular semigroup. K.S.S. Nambooripad constructed a fundamental regular semigroup by a regular biordered set abstractly. In this paper, we discuss the properties of the biordered sets of regular semigroups with inverse transversals. This kind of regular biordered sets is called IT-biordered sets. We also describe the fundamental regular semigroup TE when E is an IT-biordered set. In the sequel, we give the construction of an IT-biordered set by a left regular IT-biordered set and a right regular IT-biordered set.This project has been supported by the Provincial Natural Science Foundation of Guangdong Province, PR China |
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