On ϕ-n-absorbing primary ideals of commutative rings

2015/02/28 by Hojjat Mostafanasab, Mostafanasab, Hojjat, Ahmad Yousefian Darani +1 · 1 citation
Mathematics · #13A15 #13F05 #13G05 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13A15 #msc:13F05 #msc:13G05

paper · pdf · doi:10.48550/arxiv.1503.00108

29 pages

arxiv created 2015/02/28 · arxiv updated 2015/03/03

Abstract

All rings are commutative with 1 and n is a positive integer. Let ϕ: J(R)→ J(R)∪∅ be a function where J(R) denotes the set of all ideals of R. We say that a proper ideal I of R is ϕ-n-absorbing primary if whenever a₁,a₂,...,a_n+1∈ R and a₁a₂⋯ a_n+1∈ I\backslashϕ(I), either a₁a₂⋯ a_n∈ I or the product of a_n+1 with (n-1) of a₁,...,a_n is in √(I). The aim of this paper is to investigate the concept of ϕ-n-absorbing primary ideals.

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