On φ-δ-S-primary ideals of commutative rings
Abstract
Let R be a commutative ring with unity (1=0) and let J(R) be the set of all ideals of R. Let φ:J(R)→J(R)\\ be a reduction function of ideals of R and let δ:J(R)→J(R) be an expansion function of ideals of R. We recall that a proper ideal I of R is called a φ-δ-primary ideal of R if whenever a,b∈ R and ab∈ I-φ(I), then a∈ I or b∈δ(I). In this paper, we introduce a new class of ideals that is a generalization to the class of φ-δ-primary ideals. Let S be a multiplicative subset of R such that 1∈ S and let I be a proper ideal of R with S I=, then I is called a φ-δ-S-primary ideal of R associated to s∈ S if whenever a,b∈ R and ab∈ I-φ(I), then sa∈ I or sb∈δ(I). In this paper, we have presented a range of different examples, properties, characterizations of this new class of ideals.
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