Table of Contents Author Guidelines Submit a Manuscript
The Scientific World Journal
Volume 2013, Article ID 650702, 8 pages
http://dx.doi.org/10.1155/2013/650702
Research Article

Reversible Rings with Involutions and Some Minimalities

Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received 12 September 2013; Accepted 24 November 2013

Academic Editors: A. Badawi and Y. Lee

Copyright © 2013 W. M. Fakieh and S. K. Nauman. 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

In continuation of the recent developments on extended reversibilities on rings, we initiate here a study on reversible rings with involutions, or, in short, *-reversible rings. These rings are symmetric, reversible, reflexive, and semicommutative. In this note we will study some properties and examples of *-reversible rings. It is proved here that the polynomial rings of *-reversible rings may not be *-reversible. A criterion for rings which cannot adhere to any involution is developed and it is observed that a minimal noninvolutary ring is of order 4 and that a minimal noncommutative *-reversible ring is of order 16.