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 $n\geq 0$.
Dorostkar, F., & Yahyapour-Dakhel, M. (2022). Integral closure of a filtration relative to a Noetherian module. Journal of Algebra and Related Topics, 10(1), 129-141. doi: 10.22124/jart.2021.20320.1302
MLA
F. Dorostkar; M. Yahyapour-Dakhel. "Integral closure of a filtration relative to a Noetherian module". Journal of Algebra and Related Topics, 10, 1, 2022, 129-141. doi: 10.22124/jart.2021.20320.1302
HARVARD
Dorostkar, F., Yahyapour-Dakhel, M. (2022). 'Integral closure of a filtration relative to a Noetherian module', Journal of Algebra and Related Topics, 10(1), pp. 129-141. doi: 10.22124/jart.2021.20320.1302
VANCOUVER
Dorostkar, F., Yahyapour-Dakhel, M. Integral closure of a filtration relative to a Noetherian module. Journal of Algebra and Related Topics, 2022; 10(1): 129-141. doi: 10.22124/jart.2021.20320.1302
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