Stability in commutative rings

2020 Turkish Journal of Mathematics  
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 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
more » ... locally weakly ES-stable domain of finite character weakly ESstable?
doi:10.3906/mat-1911-101 fatcat:top4ilbdkjgpzfcfuylmwvhpai