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ON 𝜙-n-ABSORBING PRIMARY IDEALS OF COMMUTATIVE RINGS

2016
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Journal of the Korean Mathematical Society
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All rings are commutative with 1 = 0 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 a 1 , a 2 , . . . , a n+1 ∈ R and a 1 a 2 · · · a n+1 ∈ I\φ(I), either a 1 a 2 · · · an ∈ I or the product of a n+1 with (n − 1) of a 1 , . . . , an is in √ I. The aim of this paper is to investigate the concept of φ-n-absorbing primary ideals.

doi:10.4134/jkms.j150171
fatcat:7yuoq66cyvdendaoyn2s47ochu