On Wrpp Semigroups with Left Central Idempotents (1) (Report‪)‬

Abstract The relation L** on any semigroup S provides a generalization of Green's relation C. The elements a, b of S are L**-related by the rule that (ax, ay) E R [left and right arrow] (bx, by) [member of] R for all x, y [member of] [S.sup.1] where R is the usual Green's relation. A semigroup S is called a wrpp semigroup if S is a semigroup such that (i) each L**-class of S contains at least one idempotent of S; (ii) a = ae, for all e [member of] [L.sup.**.sub.a] [union] E. The aim of this paper is to investigate a wrpp semigroup with left central idempotents. It is proved that S is a wrpp semigroup with left central idempotents if and only if S is a semilattice of R-left cancellative right stripes and E(S) is a right normal band; if and only if S is a strong semilattice of R-left cancellative right stripes. Keywords wrpp semigroups, right zero bands, R-left cancellative right stripes.