n-absorbing I-primary ideals in commutative rings

2022/12/19 by Anjuman, Sarbast A., Akray, Ismael
#13A12 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2212.09883

Abstract

We define a new generalization of n-absorbing ideals in commutative rings called n-absorbing I-primary ideals. We investigate some characterizations and properties of such new generalization. If P is an n-absorbing I-primary ideal of R and √(IP) =I √(P) , then √(P) is a n-absorbing I-primary ideal of R. Also, if √(P) is an (n-1)-absorbing ideal of R such that √(I √(P)) ⊆ IP, then P is an n-absorbing I-primary ideal of R.

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