On left C-U-liberal semigroups
Yong He, Fang Shao, LI Shi-qun, Wei Dong Gao · Czechoslovak Mathematical Journal · 2006
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.