On The Properties Shared By a Simple Semigroup with an Identity and Any Semigroup with an Identity [dataset]

Invention Journals, EZE Everestus Obinwanne And 2Agwu Emeka Uchendu L.N.Ezeako
2015 Figshare  
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
more » ... an identity element which have an arbitrary cardinal number of Dclasses. These results are new extensions arising from [1].
doi:10.6084/m9.figshare.1393316.v1 fatcat:l4umlslqzbc65iv43suecpkcmu