Integral Domains in Which Every Nonzero w-Flat Ideal Is w-Invertible

Kim, Hwankoo; Lim, Jung Wook

doi:10.3390/math8020247

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Some Results On T-locally Weakly Es-stability1

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2021

2023

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“…Proof. Let I be a nonzero ideal of R. Since R is a PvMD, I w and so I is a w-flat ideal (i.e., IR P is flat for each P 2 t-MaxðRÞ) by [44,Proposition 2]. Since IR P is weakly ES-stable for each P 2 t-MaxðRÞ, I 2 R P ¼ JR P IR P for some invertible ideal JR P of R P by [8, Proposition 2.1].…”

Section: Some Results On T-locally Weakly Es-stabilitymentioning

confidence: 99%

ES-w-stability

Saylam

Hamdi

2021

Communications in Algebra

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We introduce and study the notion of ES-w-stability for an integral domain R. A nonzero ideal I of R is called ES-w-stable if ðI 2 Þ w ¼ ðJIÞ w for some tinvertible ideal J of R contained in I, and I is called weakly ES-w-stable if I w ¼ ðJEÞ w for some t-invertible fractional ideal J of R and w-idempotent fractional ideal E of R. We define R to be an ES-w-stable domain (resp., a weakly ES-w-stable domain) if every nonzero ideal of R is ES-w-stable (resp., weakly ES-w-stable). These notions allow us to generalize some well-known properties of ES-stable and weakly ES-stable domains.

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Section: Some Results On T-locally Weakly Es-stabilitymentioning

confidence: 99%