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Advances in Fuzzy Systems
Volume 2010, Article ID 258947, 4 pages
http://dx.doi.org/10.1155/2010/258947
Research Article

Two New Types of Rings Defined by Using a Translational Invariant Fuzzy Subset

Department of Mathematics, Irbid National University, P.O. Box 2600, Irbid 21110, Jordan

Received 4 March 2010; Revised 16 June 2010; Accepted 10 August 2010

Academic Editor: Eyke Huellermeier

Copyright © 2010 Manal Ghanem. 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 use a translational invariant fuzzy subset 𝑝 of a ring 𝑅 to define two new types of commutative rings namely, 𝑝 -presimplifiable and 𝑝 -associate rings. We present some results of these rings. The interest of these results is that most of them are mirrors of corresponding results of presimplifiable and associate rings in classical ring theory.