A Schreier Domain Type Condition

TL;DR

This paper investigates a specific class of integral domains where every ideal greater than a product of two ideals can be expressed as a product of larger ideals, exploring their algebraic structure.

Contribution

It introduces and characterizes a new type of domain based on a Schreier domain type condition involving ideal factorizations.

Findings

Identifies conditions under which ideals can be factored into larger ideals.

Provides structural insights into domains satisfying the Schreier type condition.

Establishes connections with known classes of integral domains.

Abstract

We study the integral domains D satisfying the following condition: whenever I >AB with I,A,B nonzero ideals, there exist ideals A'>A and B'>B such that I=A'B'.