On The Properties Shared By a Simple Semigroup with an Identity and Any Semigroup with an Identity
Journals Invention, L.N.Ezeako, Agwu Emeka Uchendu · 2015
R. H. Bruck’s theorem [1] established the fact that any semigroup S can be embedded in a Simple Semigroup which posses an identity element . In this paper, we discuss some of the properties which shares with any semigroup which posses an identity element . Thus we establish the following results i. Any regular (inverse) semigroup can be embedded in a Simple regular (Inverse) semigroup with an identity element ii. There exist simple inverse (and hence, regular) semigroups with an identity element which have an arbitrary cardinal number of D – classes. These results are new extensions arising from [1].