On Properties of Uniformly Strongly Fuzzy Ideals

Abstract

The main purpose of this paper is to continue the study of uniform strong primeness on fuzzy setting. A pure fuzzy notion of this structure allows us to develop specific fuzzy results on USP (uniformly strongly prime) ideals over commutative and noncommutative rings. Besides, the differences between crisp and fuzzy setting are investigated. For instance, in crisp setting an ideal I of a ring R is a USP ideal if the quotient R/I is a USP ring. Nevertheless, when working over fuzzy setting this is no longer valid. This paper shows new results on USP fuzzy ideals and proves that the concept of uniform strong primeness is compatible with a-cuts. Also, the Zadeh's extension under epimorphisms does not preserve USP ideals. Finally, the t- and m- systems are introduced in a fuzzy setting and their relations with fuzzy prime and uniformly strongly prime ideals are investigated.