Stability in Commutative Rings | Zendy

Başak Ay Saylam | Zendy

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Stability in Commutative Rings

Author(s) -

Başak Ay Saylam

Publication year - 2020

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1911-101

Subject(s) - mathematics , ideal (ethics) , invertible matrix , pure mathematics , idempotence , primary ideal , noetherian , noetherian ring , commutative property , commutative ring , stability (learning theory) , von neumann regular ring , maximal ideal , ring (chemistry) , discrete mathematics , principal ideal ring , algebra over a field , law , chemistry , organic chemistry , machine learning , political science , computer science

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?

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