The Green~(e)-relations on semigroups
LI Shun-bo · 2008
The Green~(e)-relations are generalizations of the usual Green's-relations on a semigroup.By using left(right)S-systems and bisystems for a semigroup S,we describe the algerbric properties of Green~(e)-relations on any semigroup S and show that every H~(e)-class R_e~(e)∩L_f~(e)of a semigroup S is a strongly torsion-free (H_e~(e),H_f~(e)-bisystem for any idempotents e,f of S.Also,we eastablish the algerbric structure for any D~(e)-class containing idernpotent of a semigroup S.