# Commutative Rings with Two-Absorbing Factorization

## TL;DR

This paper investigates commutative rings where every proper ideal factors into 2-absorbing ideals, revealing structural properties and classifying local cases as atomic pseudo-valuation domains.

## Contribution

It introduces TAF-rings, characterizes their dimension, and identifies local TAF-domains as atomic pseudo-valuation domains.

## Key findings

- TAF-rings have dimension at most one.
- Local TAF-domains are atomic pseudo-valuation domains.
- Every proper ideal in a TAF-ring factors into 2-absorbing ideals.

## 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.