Factoring ideals and stability in integral domains

Abstract

In an integral domain $R$, a nonzero ideal is called a \textit {weakly $ES$-stable ideal} if it can be factored into a product of an invertible ideal and an idempotent ideal of $R$; and $R$ is called a \textit {weakly $ES$-stable domain} if every nonzero ideal is a weakly $ES$-stable ideal. This paper studies the notion of weakly $ES$-stability in various contexts of integral domains such as Noetherian and Mori domains, valuation and Pr\"ufer domains, pullbacks and more. In particular, we establish strong connections between this notion and well-known stability conditions, namely, Lipman, Sally-Vasconcelos and Eakin-Sathaye stabilities.