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The Scientific World Journal
Volume 2014 (2014), Article ID 413564, 7 pages
http://dx.doi.org/10.1155/2014/413564
Research Article

The Lattices of Group Fuzzy Congruences and Normal Fuzzy Subsemigroups on -Inversive Semigroups

Department of Mathematics, Yunnan Normal University, Kunming, Yunnan 650500, China

Received 28 February 2014; Revised 23 April 2014; Accepted 23 April 2014; Published 5 May 2014

Academic Editor: Luis Martínez

Copyright © 2014 Shoufeng Wang. 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

The aim of this paper is to investigate the lattices of group fuzzy congruences and normal fuzzy subsemigroups on -inversive semigroups. We prove that group fuzzy congruences and normal fuzzy subsemigroups determined each other in -inversive semigroups. Moreover, we show that the set of group -fuzzy congruences and the set of normal subsemigroups with tip in a given -inversive semigroup form two mutually isomorphic modular lattices for every .