Journal of Commutative Algebra

A short proof of a result of Katz and West

Dipankar Ghosh and Tony J. Puthenpurakal

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Abstract

We give a short proof of a result due to Katz and West: Let $R$ be a Noetherian ring and $I_1,\ldots ,I_t$ ideals of $R$. Let $M$ and $N$ be finitely generated $R$-modules and $N' \subseteq N$ a submodule. For every fixed $i \ge 0$, the sets $$ \mathrm {Ass}_R(\mathrm {Ext}_R^i(M,N/I_1^{n_1}\cdots I_t^{n_t} N') ) $$ and $$ \mathrm {Ass}_R(\mathrm {Tor}_i^R(M,N/I_1^{n_1}\cdots I_t^{n_t} N') ) $$ are independent of $(n_1,\ldots ,n_t)$ for all sufficiently large $n_1,\ldots ,n_t$.

Article information

Source
J. Commut. Algebra, Volume 11, Number 2 (2019), 237-240.

Dates
First available in Project Euclid: 24 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.jca/1561363359

Digital Object Identifier
doi:10.1216/JCA-2019-11-2-237

Mathematical Reviews number (MathSciNet)
MR3973138

Zentralblatt MATH identifier
07080076

Subjects
Primary: 13E05: Noetherian rings and modules 13D07: Homological functors on modules (Tor, Ext, etc.)
Secondary: 13A15: Ideals; multiplicative ideal theory 13A30: Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics

Keywords
Associate primes Rees ring Ext Tor

Citation

Ghosh, Dipankar; Puthenpurakal, Tony J. A short proof of a result of Katz and West. J. Commut. Algebra 11 (2019), no. 2, 237--240. doi:10.1216/JCA-2019-11-2-237. https://projecteuclid.org/euclid.jca/1561363359


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References

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