Advanced Search

In this paper the equivalence ${\widetilde{𝒬}}^U$ 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 $S\left(U\right)$ if every ${\widetilde{𝒬}}^U$-class in it contains an element in $U$. A class of $𝒰$-liberal semigroups is characterized and some special cases are considered.