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We first establish the following lemmas of left-e wrpp semigroups:
If S is a left-e wrpp semigroup, then every [L.sup.**]-class of S contains a unique idempotent.
Since S is a left-e wrpp semigroup, [a.sup.+] a = a = [aa.sup.+] for all a [member of] S.
If S is a left-e wrpp semigroup, then [L.sup.**] is a congruence on S.
We now define the following right E-balanced relation [gamma] on a left-e wrpp semigroup.
Let S be a left-e wrpp semigroup and let a, b [member of] S.
If S is a wrpp semigroup with left central idempotents, then [(ab).sup.+] = [a.sup.+][b.sup.+] for all a, b [member of] S.
We now define a binary relation [sigma] on a wrpp semigroup S with left central idempotents by
We are now able to describe the wrpp semigroups with left central idempotents by using R-left cancellative right stripes.
Now we come to our main result for the construction of wrpp semigroups with left central idempotents.
If S is a wrpp semigroup with left central idempotents and [S.sub.[alpha]] is any [sigma]-class of S, then [S.sub.[alpha]] can be expressed as a direct product of R-left cancellative monoid and a right zero band.
To prove that (1) holds, we still need to show that S is a wrpp semigroup.
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