Subsemigroups of simple semigroups
Štefan Schwarz · Czechoslovak Mathematical Journal · 1963
The purpose of this paper is to study the structure of subsemigroups of a simple semigroup 5, especially in the case when S is completely simple.Also coset decompositions of S modulo some subsemigroups are studied.Let S be a semigroup.A left ideal of S is a subset Lcz S with SLcz L. A right ideal of S is a subset R with RS a R. A subset which is both a left and right ideal of S is called a two-sided ideal of S.The semigroup S itself and the zero element 0 (if S contains a zero element) are always two-sided ideals.A minimal left ideal of S is a left ideal of S which does not contain any proper left ideal of S with the eventually exception of (0) (if S contains a zero element).Minimal right and two-sided ideals are defined analogously.A semigroup S without zero and containing at least two elements is called simple if it does not contain any two-sided ideal ф S.