MODULARITY OF AJMAL FOR THE LATTICES OF FUZZY IDEALS OF A RING

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 lattice  \vartheta(R) of all fuzzy ideals of a ring R is modular.

کلیدواژه ها:

Algebra ، Lattice ، Modularity ، Ideal of a ring ، Morphism