Abstract

It is well known that the rpp semigroups are generalized regular semigroups. In order to further investigate the structure of rpp semigroups, we introduce the type-(I, L ∗ ) factorizable monoids. In this paper, we study such factorizable rpp monoids admitting a left univocal type-(I, L ∗ ) factorization. In particular, we prove that a semigroup S is a factorizable rpp monoid admitting a left univocal type-(I, L ∗ ) factorization if and only if S is isomorphic to a semidirect product of a band and a left cancellative monoid. Some results of Catino and Tolo on factorizable semigroups are extended and amplified.

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