Semigroups decomposable into a semilattice of Archimedean semigroups, having certain additional properties such as the intra-, left, right and complete π-regularity, have been investigated in many papers. In the present paper, we study the π-regular ones. Among other things, we characterize them as semilattices of nil-extensions of simple regular semigroups. The obtained results generalize some results given by Munn, Putcha, Shevrin, Bogdanović, Ćirić, and others.
Algebra Colloquium – Springer Journals
Published: Jan 1, 2003