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On left C-U-liberal semigroups

Authors:	Yong He Fang Shao Shi-qun Li Wei Gao

Institution:	(1) School of Computer, Hunan University of Science & Technology, Xiangtan, Hunan, 411201, P. R. China;(2) Department of Scientific Reserch, Hunan University of Science & Technology, Xiangtan, Hunan, 411201, P. R. China;(3) School of Mathematics, Hunan University of Science & Technology, Xiangtan, Hunan, 411201, P. R. China;(4) Department and Institute of Mathematics, Fudan university, Shanghai, P. R. China

Abstract:	In this paper the equivalence $\tilde {\cal Q}^U$ on a semigroup S in terms of a set U of idempotents in S is defined. A semigroup S is called a U-liberal semigroup with U as the set of projections and denoted by S(U) if every $\tilde {\cal Q}^U$ -class in it contains an element in U. A class of U-liberal semigroups is characterized and some special cases are considered.

Keywords:	" target="_blank">equivalence gif" alt=" $$\tilde {\cal Q}^U $$ " target="_blank">" align="middle" border="0"> left C-U-liberal semigroup left semi-spined product band-formal construction left C-liberal semigroup
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