Abstract
In this work, we give a characterization of generalizations of prime and primary fuzzy ideals by introducing 2-absorbing fuzzy ideals and 2-absorbing primary fuzzy ideals and establish relations between 2-absorbing (primary) fuzzy ideals and 2-absorbing (primary) ideals. Furthermore, we give some fundamental results concerning these notions.
Highlights
The fundamental concept of fuzzy set was introduced by Zadeh [1] in 1965
Prime ideals and primary ideals play a significant role in commutative ring theory
The concept of 2-absorbing ideals, which is a generalization of prime ideals [4], and the concept of 2-absorbing primary ideals, which is a generalization of primary ideals [5], were introduced
Summary
The fundamental concept of fuzzy set was introduced by Zadeh [1] in 1965. In 1982, Liu introduced the notion of fuzzy ideal of a ring [2]. Prime ideals and primary ideals play a significant role in commutative ring theory. Because of this importance, the concept of 2-absorbing ideals, which is a generalization of prime ideals [4], and the concept of 2-absorbing primary ideals, which is a generalization of primary ideals [5], were introduced. If μ is 2-absorbing primary fuzzy ideal of R, which is constant on Ker f, it is proved that f(μ) is a 2-absorbing primary fuzzy ideal of S It is shown under what condition the intersection of the collection of 2-absorbing primary fuzzy ideals is 2-absorbing primary fuzzy ideal. It is proved that union of a Mathematical Problems in Engineering directed collection of 2-absorbing primary fuzzy ideals of R is 2-absorbing primary fuzzy ideal
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