Abstract
We study the strongly rpp-semigroups whose set of idempotents forms a right regular band and the relation ${\cal L}^* \vee {\cal R}$ is a congruence. This kind of strongly rpp-semigroups was called by Y.Q. Guo the right C-rpp semigroups and he characterized them as semilattice of direct products of left cancellative monoid with right zero semigroup. The aim of this paper is to improve upon Guo’s result, giving a tighter description of the semilattice decomposition involving a system of connecting maps. By using our result, we can always construct a right C-rpp semigroup by glueing up the given ingredients by the connecting maps. An example of an infinite right C-rpp semigroup is constructed.
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