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Advances in Mathematical Physics
Volume 2016, Article ID 6423735, 6 pages
http://dx.doi.org/10.1155/2016/6423735
Research Article

Characterizations of Fuzzy Ideals in Coresiduated Lattices

1College of Science, Xi’an University of Science and Technology, Xi’an 710054, China
2School of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710119, China

Received 27 January 2016; Revised 30 June 2016; Accepted 3 July 2016

Academic Editor: Remi Léandre

Copyright © 2016 Yan Liu and Mucong Zheng. 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 notions of fuzzy ideals are introduced in coresiduated lattices. The characterizations of fuzzy ideals, fuzzy prime ideals, and fuzzy strong prime ideals in coresiduated lattices are investigated and the relations between ideals and fuzzy ideals are established. Moreover, the equivalence of fuzzy prime ideals and fuzzy strong prime ideals is proved in prelinear coresiduated lattices. Furthermore, the conditions under which a fuzzy prime ideal is derived from a fuzzy ideal are presented in prelinear coresiduated lattices.