Stability in Commutative Rings

Abstract

Let R be a commutative ring with zero-divisors and I an ideal of R. I is said to be ES-stable if JI = $I^2$for some invertible ideal J ⊆ I , and I is said to be a weakly ES-stable ideal if there is an invertible fractional ideal J andan idempotent fractional ideal E of R such that I = JE . We prove useful facts for weakly ES-stability and investigatethis stability in Noetherian-like settings. Moreover, we discuss a question of A. Mimouni on locally weakly ES-stablerings: is a locally weakly ES-stable domain of finite character weakly ES-stable?