International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 763428, 9 pages
http://dx.doi.org/10.1155/2012/763428
Research Article

Nilpotent Elements of Residuated Lattices

Shokoofeh Ghorbani1 and Lida Torkzadeh2

1Department of Mathematics, Bam Higher Education Complexes, Kerman, Iran
2Department of Mathematics, Islamic Azad University, Kerman Branch, Kerman, Iran

Received 28 March 2012; Revised 13 June 2012; Accepted 27 June 2012

Academic Editor: Siegfried Gottwald

Copyright © 2012 Shokoofeh Ghorbani and Lida Torkzadeh. 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

Some properties of the nilpotent elements of a residuated lattice are studied. The concept of cyclic residuated lattices is introduced, and some related results are obtained. The relation between finite cyclic residuated lattices and simple MV-algebras is obtained. Finally, the notion of nilpotent elements is used to define the radical of a residuated lattice.