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Decomposition of ideals into pseudo-irreducible ideals
Authors:Sina Hedayat
Affiliation:Department of Pure Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran
Abstract:
A proper ideal of a commutative ring is called pseudo-irreducible if it cannot be written as a product of two comaximal proper ideals. In this paper, we give a necessary and su?cient condition for every proper ideal of a commutative ring to be a product of pairwise comaximal pseudo-irreducible ideals. Examples of such rings include Laskerian rings, or more generally J-Noetherian rings and ZD-rings. We study when certain classes of rings satisfy this condition.
Keywords:CIFR  complete comaximal factorization  Laskerian rings  pseudo-irreducible ideal  Zariski topology
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