ON SOME REGULAR SUBSEMIGROUPS OF SEMIGROUPS
Niovi Kehayopulu, Michael Tsingelis · Scientiae mathematicae Japonicae · 2010
For a subsemigroup T of a semigroup S, Reg(T ) denotes the set of regular elements of T , LReg(T ) the set of left regular elements of T and reg(T ) the set of elements of T which are regular in S. Characterizations of a semigroup S for which reg(Se) = Reg(Se) for each idempotent element e of S have been given in [3]. This type of semigroups is the semigroups S in which each element of the subsemigroup Se of S which is regular in S is a left regular element of Se for every idempotent element e of S. Moreover, this type of semigroups is the semigroups S in which the regular elements are left regular, equivalently the sets of regular and completely regular elements coincide [3]. In the present paper we prove that the type of semigroups mentioned above is actually the semigroups in which reg(Sa) = reg(Sa) for every a ∈ S.