A new structure theorem of left C-wrpp semigroups
Xiaoming Ren, Xiuyong Ding, K. P. Shum · International Journal of Algebra · 2007
Semi-spined product structure of a left C-wrpp semigroup has been recently described by Du and Shum. In this paper, we will introduce a new concept,namely the left cross product of semigroups and establish a new structure theorem for the left C-wrpp semigroup by using left cross product. It is shown that a semigroup S is a left C-wrpp semigroup if and only if S can be expressed as a left cross product of a left regular band I and an C-wrpp semigroup M which is a strong semilattice of left R-cancellative monoids.This theorem generalizes the classical structure theorem of C-rpp monoids obtained by Fountain in 1977.