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 $J \subseteq I$, and $I$ is said to be a weakly ES-stable ideal if there is an invertible fractional ideal $J$ and an idempotent fractional ideal $E$ of $R$ such that $I=JE$. We prove useful facts for weakly ES-stability and investigate this stability in Noetherian-like settings. Moreover, we discuss a question of A. Mimouni on locally weakly ES-stable rings: is a locally weakly ES-stable domain of finite character weakly ES-stable?
Weakly ES-stable rings, Prüfer rings, H-local rings, Local-global rings, Noetherian rings.
SAYLAM, BAŞAK AY
"Stability in Commutative Rings,"
Turkish Journal of Mathematics: Vol. 44:
3, Article 13.
Available at: https://journals.tubitak.gov.tr/math/vol44/iss3/13