On (m,n) - Separative EMBEDDING THEOREMS ON SEMIGROUPS

Abstract

In this püper we investigate some embedding problems on semigroups. In Section 2 we give necessary and sufficicient conditions for semigroups to be embeddable in right groups. We give a criterion for semigroups with zero element to be embeddable in semigroups having a zero element 0 and being unions of disjoint subgroup G_α, αeY, such that G_α G_β=0if α≠β. in Section 3 we investigate the enihedd.iag of commutative semigroups into groups, in particular, into torsion-free groups. For this purpose we define (m,n)-separativity of semigroups. In Section- 4 (m,n)-separative semigroups will be studied.

For all notationa and notione which are not defined in this paper, we refer to [1].