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 Fattahi1
, Mohamad Ali Pourabdollah2
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
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.