Regularity and Archimedeaness of Semidirect Products of Semigroups
by
Žarko Popović
University of Niš, Niš, Yugoslavia
Coauthors: Stojan Bogdanović (University of Niš), Miroslav Ćirić (University of Niš)

Since 1960's, when semidirect products of semigroups were introduced by B. H. Neumann, they have been a subject of interest of numerous semigroup theoreticians and they have had a lot of significant applications in many areas of Semigroup theory. One of the most frequently stated questions concerning semidirect product was the following: Under which conditions a semidirect product of two semigroups has a given property? As for example, problems of that type have been treated by A. Batbedat (1979), V. M. Usenko (1982), W. R. Nico (1983), G. B. Preston (1986), R. G. Wilkinson (1986), T. Saito (1989), F. Catino and M. Micoli (1989), B. Stamenkovi\'c (1995), R. Zhang (1999) and others.

The central place in these investigations has been captured by semidirect products which are regular. One of the main aims of this paper is to study semidirect products that have various properties more general than the regularity. Namely, we consider semidirect products of semigroups which are left, right, intra or completely \pi-reproduced, or left, right, intra or completely quasi \pi-regular etc. On the other hand, we also study semidirect products belonging to various subclasses of the class of Archimedean semigroups, such as (left, right) strict Archimedean, (left, right) completely Archimedean, \pi-regular Archimedean semigroups etc.

Date received: May 9, 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-22.