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Abstract and Applied Analysis
Volume 2014, Article ID 309708, 6 pages
Research Article

On the Covariance of Moore-Penrose Inverses in Rings with Involution

Department of Mathematics, Islamic Azad University, Firoozkooh Branch, Firoozkooh, Iran

Received 17 February 2014; Revised 14 April 2014; Accepted 14 April 2014; Published 5 May 2014

Academic Editor: Sergei V. Pereverzyev

Copyright © 2014 Hesam Mahzoon. 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.


We consider the so-called covariance set of Moore-Penrose inverses in rings with an involution. We deduce some new results concerning covariance set. We will show that if is a regular element in a -algebra, then the covariance set of is closed in the set of invertible elements (with relative topology) of -algebra and is a cone in the -algebra.