On \pi-semisimple and Left Quasi-\pi-regular Semigroups
by
Melanija Mitrovic
University of Nis, Nis, Yugoslavia

Semisimple semigroups are known as semigroups which have very significant applications in theories of semigroup algebras and representations of semigroups and algebras by matrices over a field. From that reason they were studied by W. D. Munn, and later by many other authors. In 1974, G. Szász characterized them as semigroups S in which a in SaSaS, for every a in S. An important special case of these semigroups are left quasi-regular semigroups , defined by J. Callais in 1961 as semigroups S in which a in SaSA, for any a in S. In order to generalize the notion of a semisimple semigroup, E. Hotzel in 1975 defined a semigroup S to be weakly periodic , or in our terminology \pi-semisimple , if every a in S has a power aⁿ satisfying aⁿ in SaⁿSaⁿS. Here we introduce the notion of a left quasi-\pi-regular semigroup, which is defined as a semigroup S in which any a in S has a power aⁿ for which aⁿ in SaⁿSaⁿ.

The main our goal is to study various structural properties of \pi-semisimple and left quasi\pi-regular semigroups. Much attention is aimed to their semilattice decompositions, especially to the ones with archimedean components. The obtained results generalize many results in this area given by W. D. Munn, M. S. Putcha, R. Croisot, M. L. Veronesi, L. N. Shevrin, S. Bogdanovi\'c, M. \'Ciri\'c, M. Mitrovi\'c and others.

Date received: May 12, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caec-29.