Table of Contents
Algebra
Volume 2013 (2013), Article ID 452862, 3 pages
http://dx.doi.org/10.1155/2013/452862
Research Article

On -Cogenerated Commutative Unital -Algebras

Department of Mathematics, Yasouj University, Yasouj, Iran

Received 22 November 2012; Accepted 17 May 2013

Academic Editor: Xueqing Chen

Copyright © 2013 Ehsan Momtahan. 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

Gelfand-Naimark's theorem states that every commutative -algebra is isomorphic to a complex valued algebra of continuous functions over a suitable compact space. We observe that for a completely regular space , is dense- -separable if and only if is -cogenerated if and only if every family of maximal ideals of with zero intersection has a subfamily with cardinal number less than and zero intersection. This gives a simple characterization of -cogenerated commutative unital -algebras via their maximal ideals.