Decomposition of ideals into pseudo-irreducible ideals

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 sufficient 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

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 13A15

Acknowledgments

The authors gratefully acknowledge the constructive comments on this paper offered by the anonymous referee. We express our sincere gratitude for his/her review, which helped to improve the quality of the paper significantly.