Linearly equivalent topologies and locally quasi-unmixed rings

Temel Bulgular & Veri:The main result of this paper asserts that $R$ is locally quasi-unmixed if and only if, the topologies defined by $\overline{I^n}$ and $I^{\langle n\rangle}$, $\ n\geq 1$, are equivalent.

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Sonuç & Katkı:In addition, some results about the behavior of linearly equivalent topologies of ideals under various ring homomorphisms are included.

🔬Tür:Araştırma Makalesi

📍Kapsam:Genişletilmiş Akademik Örneklem

⚙️Değişkenler:associated primes · linearly equivalent topologies · integral closure

Abstract

Let $\bar{I}$ denote the integral closure of an ideal in a Noetherian ring $R$. The main result of this paper asserts that $R$ is locally quasi-unmixed if and only if, the topologies defined by $\overline{I^n}$ and $I^{\langle n\rangle}$, $\ n\geq 1$, are equivalent. In addition, some results about the behavior of linearly equivalent topologies of ideals under various ring homomorphisms are included.

Anahtar kelimeler

associated primes linearly equivalent topologies integral closure locally quasi-unmixed ring Rees ring

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Bu Makaleye Atıf Yap

AZARİ, A., MOLLAMAHMOUDİ, S., NAGHİPOUR, R. (2019). Linearly equivalent topologies and locally quasi-unmixed rings. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 4, 1131–1136. https://ajindex.com/articles/669347

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Kaynakça (12)

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