Extensions of semigroups by symmetric inverse semigroups of a~bounded finite rank
Олег Гутік, Oleksanadra Sobol · Visnyk Lvivskogo Universytetu Seriya Mekhaniko-Matematychna · 2020
transformations, Green's relations, semigroup has a tight ideal series, semitopologica; semigroup, compact semigroup. Introduction, motivation and main definitionsIn this paper we follow the terminology of [11,31].If S is a semigroup, then by E(S) we denote the subset of all idempotents of S. On the set of idempotents E(S) there exists the natural partial order: e f if and only if ef = f e = e.A semigroup S is called:• regular, if for every a ∈ S there exists an element b in S such that a = aba;• orthodox, if S is regular and E(S) is a subsemigroup of S;