Abstract
The concepts of fuzzy semi-ideals of R with respect to HR ≤ and generalized fuzzy quotient rings are introduced. Some properties of fuzzy semi- ideals are discussed. Finally, several isomorphism theorems for generalized fuzzy quotient rings are established. 1. Preliminaries Since the concept of fuzzy subgroups was introduced by Rosenfeld (6) in 1971, the literature of these fuzzy algebraic concepts has been growing very rapidly. Liu (4) defined and studied fuzzy subrings as well as fuzzy ideals in rings. Subsequently, Mukherjee and Sen (5), and Zhang (7) further various fuzzy characterized ideals in rings. Based on the concept of fuzzy ideal, Kumbhojkar and Bapat (3) introduced the concept of fuzzy quotient ring and established the correspondence theorems for fuzzy ideals. In this paper, we first generalize the concepts of fuzzy ideals and fuzzy quotient rings and then establish several isomorphism theorems for generalized fuzzy quotient rings.
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