The relation L** on any semigroup S provides a generalization of Green's relation L. The elements a, b of S are L**-related by the rule that (ax, ay)∈ R (→)(bx, by) ∈R for all x, y ∈S1 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 L**a ∩ 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 semilattiee of R-left caneellative right stripes.
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