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.

💡

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

🔬Tür:Research Article

📍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

🔖

Bu Makaleye Atıf Yap

Azari, A., Mollamahmoudi, S., Naghipour, R. (2019). Linearly equivalent topologies and locally quasi-unmixed rings. Hacettepe Journal of Mathematics and Statistics, Volume: 48 Issue: 4. https://ajindex.com/articles/1402768

📄 Tam Metin PDF Okuyucu

Yeni Sekmede Aç ↗

↗Yeni Sekme

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (12)

H. Matsumura, Commutative Ring Theory, Cambridge University Press, 1986.
S. McAdam, Asymptotic Prime Divisors, Lecture Notes in Math. 1023, Springer- Verlag, New York, 1983.
S. McAdam, Quintasymptotic primes and four results of Schenzel, J. Pure Appl. Algebra 47, 283–298, 1987.
S. McAdam and L. J. Ratliff Jr., On the asymptotic cograde of an ideal, J. Algebra 87, 36–52, 1984.
M. Nagata, Local Rings, Interscience, New York, 1961.
R. Naghipour, Locally unmixed modules and ideal topologes, J. Algebra 236, 768–777, 2001.
D.G. Northcott and D. Rees,Reductions of ideals in local rings, Proc. Cambridge Philos. Soc. 50, 145–158, 1954.
L.J. Ratliff Jr., Asymptotic sequences, J. Algebra 85, 337–360, 1983.
L.J. Ratliff Jr., On asymptotic prime divisors, Pacific J. Math. 111, 395–413, 1984.
L.J. Ratliff Jr., Asymptotic prime divisors and integral extension rings, J. Algebra 95, 409–431, 1985.
D. Rees, A note on analytically unramified local rings, J. London Math. Soc. 36, 24–28, 1961.
J.K. Verma, On ideals whose adic and symbolic topologies are linearly equivalent, J. Pure Appl. Algebra 47, 205–212, 1987.