Semilattices of nil-extensions of simple left (right) $\pi$-regular ordered semigroups


QingShun Zhu




The purpose of this paper is to describe the semilattice of nil-extensions of simple left (right) $\pi$-regular ordered semigroups. We will divide this discussion into two parts. In the first part we will give the characterizations of semilattice of nil-extensions of simple left (right) $\pi$-regular ordered semigroups. As applications, in the second part we characterize nil-extensions of simple completely $\pi$-regular ordered semigroups.