Integral closure of a filtration relative to a Noetherian module

	Integral closure of a filtration relative to a Noetherian module
Journal of Algebra and Related Topics
دوره 10، شماره 1، شهریور 2022، صفحه 129-141 اصل مقاله (290.2 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22124/jart.2021.20320.1302
نویسندگان
F. Dorostkar^* ؛ M. Yahyapour-Dakhel
Department of Pure Mathematics, University of Guilan, Rasht, Iran
چکیده
Let $M$ be a Noetherian $R-$module. In this paper we will introduce the integral closure of a filtration ${\mathcal{F}}=\{I_{n}\}_{n\geq 0}$ relative to the Noetherian module $M$ and prove some related results.\\ The integral closure of a filtration ${\mathcal{F}}=\{I_{n}\}_{n\geq 0}$ relative to $M$ is a filtration and it has an interesting relationship with the integral closure of the filtration ${\widetilde{\mathcal{F}}}=\{\widetilde{I}_{n}\}_{n\geq 0}$, where $\widetilde{I}_{n}$ is the image of $I_n$ under the natural ring homomorphism $R\rightarrow R/(Ann_R(M))$ for every $n\geq 0$.
کلیدواژه‌ها
Filtration؛ Reduction of a filtration؛ Noetherian filtration؛ Integral closure of a filtration

آمار تعداد مشاهده مقاله: 477 تعداد دریافت فایل اصل مقاله: 353

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