Dual Wreath Product Structure of Right C-rpp Semigroups

Abstract

The concept of wreath product of semigroups was initiated by Neumann in 1960, and later on, his concept was used by Preston to investigate the structure of some inverse semigroups. Recently, we start to investigate the structure of left C-rpp semigroups by using wreath products. In this paper, we modify the wreath product to “dual wreath product” so that we can study the structure of right C-rpp semigroups. We prove that a semigroup is a right C-rpp semigroup if and only if it is the dual wreath product of a right regular band and a C-rpp semigroup. Our theorem provides new insight to the structure of right C-rpp semigroups. In particular, a recent result given by Ren and Shum for right C-rpp semigroups is strengthened and enriched.