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.
Maji et al. introduced the concept of intuitionistic fuzzy soft sets, which is an extension of soft sets and intuitionistic fuzzy sets. In this paper, we apply the concept of intuitionistic fuzzy soft sets to rings. The concept of intuitionistic fuzzy soft rings is introduced and some basic properties of intuitionistic fuzzy soft rings are given. Intersection, union, AND, and OR operations of intuitionistic fuzzy soft rings are defined. Then, the deffinitions of intuitionistic fuzzy soft ideals are proposed and some related results are considered.
In this paper, the definitions of soft Γ-semirings and soft sub Γ-semi rings are introduced with the aid of the concept of soft set theory introduced by Molodtsov. In the mean time, some of their properties and structural characteristics are investigated and discussed. Thereafter, several illustrative examples are given.
This paper aims to introduce 2-absorbing φ -δ -primary ideals over commutative rings which unify the concepts of all generalizations of 2-absorbing and 2-absorbing primary ideals. Let A be a commutative ring with a nonzero identity and I(A) be the set of all ideals of A . Suppose that δ : I(A) → I(A) is an expansion function and φ : I(A) → I(A)∪{∅} is a reduction function. A proper ideal Q of A is said to be a 2-absorbing φ -δ -primary if whenever abc ∈ Q − φ(Q) , where a, b, c ∈ R, then either ab ∈ Q or ac ∈ δ(Q) or bc ∈ δ(Q). Various examples, properties and characterizations of this new class of ideals are given.
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