2022/07/05 by Jaber, Ameer
#13A05 #13A15 #13A99 #13C05 #Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2207.02065
Let R be a commutative ring with unity (1\not=0) and let \mathfrakJ(R) be the set of all ideals of R. Let ϕ:\mathfrakJ(R)→\mathfrakJ(R)∪\∅\ be a reduction function of ideals of R and let δ:\mathfrakJ(R)→\mathfrakJ(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.