Stability in Commutative Rings
Authors : Başak Ay Saylam
Pages : 801-812
Doi:10.3906/mat-1911-101
View : 8 | Download : 4
Publication Date : 9999-12-31
Article Type : Makaleler
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 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?Keywords : Weakly ES-stable rings, Prüfer rings, H-local rings, Local-global rings, Noetherian rings.