On Semilattices of R-Ample Semigroups with Left Central Idempotents
Yan Sun · Applied Mechanics and Materials · 2014
In this article, the semilattice decomposition of r-ample semigroups with left central idempotents is given. By using this decomposition, we show that a semigroup is a r-ample semigroup with left central idempotents if and only if it is a strong semilattice of , where is a monoid and is a right zero band. As a corollary, the characterization theorem of Clifford semigroups is also extended from a strong semilattice of groups to a strong semilattice of right groups. These theories are the basis that the structure theorem of r-ample semigroups with left central idempotents can be established.