Some Conditions of Equivalence about Sem igroups with Inverse Transversals
Luo Min-xia · 2006
In this paper,we introduce a Green relation which is 0-Green relation.This paper studied semigroups with inverse transversals by a new research method—enlargement,which is about regular semigroups by Lawson.Some conditions of equivalence of semigroups with inverse transversals was given.We prove that S~) is an inverse transversal of semigroup S if and only if each R~0-class of P={e∈S;(e′∈V(e)∩S~0)ee′=e} contains an unique idempotent,and each L~0-class of Q={f∈S;(f′∈V(f)∩S~0)f′f=f} contains an unique idempotent.