Commutative rings with two-absorbing factorization

ABSTRACT

We use the concept of 2-absorbing ideal introduced by Badawi to study those commutative rings in which every proper ideal is a product of 2-absorbing ideals (we call them TAF-rings). Any TAF-ring has dimension at most one and the local TAF-domains are the atomic pseudo-valuation domains.

KEYWORDS:

• Dedekind domain
• pseudo-valuation domain
• two-absorbing ideal

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 13A15
• Secondary: 13F15

Acknowledgments

We thank the referee whose suggestions improved our paper. The first two authors are highly grateful to ASSMS, GC University, Lahore, Pakistan in supporting and facilitating this research. The third author gratefully acknowledges the warm hospitality of Abdus Salam School of Mathematical Sciences, GC University, Lahore during his visits in the period 2006–2016.