%0 Journal Article
%T MODULARITY OF AJMAL FOR THE LATTICES OF FUZZY IDEALS
OF A RING
%J Iranian Journal of Fuzzy Systems
%I University of Sistan and Baluchestan
%Z 1735-0654
%A JAHAN, IFFAT
%D 2008
%\ 06/08/2008
%V 5
%N 2
%P 71-78
%! MODULARITY OF AJMAL FOR THE LATTICES OF FUZZY IDEALS
OF A RING
%K Algebra
%K Lattice
%K Modularity
%K Ideal of a ring
%K Morphism
%R 10.22111/ijfs.2008.335
%X In this paper, we construct two fuzzy sets using the notions of level subsets and strong level subsets of a given fuzzy set in a ring R. These fuzzy sets turn out to be identical and provide a universal construction of a fuzzy ideal generated by a given fuzzy set in a ring. Using this construction and employing the technique of strong level subsets, we provide the shortest and direct fuzzy set theoretic proof of the fact that the latticeĀ $vartheta$(R) of all fuzzy ideals of a ring R is modular.
%U https://ijfs.usb.ac.ir/article_335_d77ea108880da9b02b705e6c27df1d4f.pdf