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2017 Sequentially Cohen-Macaulayness of bigraded modules
Ahad Rahimi
Rocky Mountain J. Math. 47(2): 621-635 (2017). DOI: 10.1216/RMJ-2017-47-2-621

Abstract

Let $K$ be a field, $S=K[x_1,\ldots ,x_m, y_1,\ldots , y_n]$ a standard bigraded polynomial ring, and $M$ a finitely generated bigraded $S$-module. In this paper, we study the sequentially Cohen-Macaulayness of~$M$ with respect to $Q=(y_1,\ldots ,y_n)$. We characterize the sequentially Cohen-Macaulayness of $L\otimes _KN$ with respect to $Q$ as an $S$-~module when $L$ and $N$ are non-zero finitely generated graded modules over $K[x_1, \ldots , x_m]$ and $K[y_1, \ldots , y_n]$, respectively. All hypersurface rings that are sequentially Cohen-Macaulay with respect to $Q$ are classified.

Citation

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Ahad Rahimi. "Sequentially Cohen-Macaulayness of bigraded modules." Rocky Mountain J. Math. 47 (2) 621 - 635, 2017. https://doi.org/10.1216/RMJ-2017-47-2-621

Information

Published: 2017
First available in Project Euclid: 18 April 2017

zbMATH: 06715764
MathSciNet: MR3635377
Digital Object Identifier: 10.1216/RMJ-2017-47-2-621

Subjects:
Primary: 13C14, 13D45, 16W50, 16W70

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 2 • 2017
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