International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 51, Pages 3277-3280
doi:10.1155/S0161171203202052

Reductive compactifications of semitopological semigroups

Abdolmajid Fattahi,1 Mohamad Ali Pourabdollah,2 and Abbas Sahleh3

1Department of Mathematics, Faculty of Science, Razi University, Kermanshah, Iran
2Faculty of Mathematics, Ferdowsi University of Mashhad, P.O. Box 91775-1159, Mashhad, Iran
3Department of Mathematics, Guilan University, Rasht, Iran

Received 10 February 2002

Copyright © 2003 Abdolmajid Fattahi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the enveloping semigroup of a flow generated by the action of a semitopological semigroup on any of its semigroup compactifications and explore the possibility of its being one of the known semigroup compactifications again. In this way, we introduce the notion of E-algebra, and show that this notion is closely related to the reductivity of the semigroup compactification involved. Moreover, the structure of the universal Eℱ-compactification is also given.