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2018 Unimodular elements in projective modules and an analogue of a result of Mandal
Manoj K. Keshari and Md. Ali Zinna
J. Commut. Algebra 10(3): 359-373 (2018). DOI: 10.1216/JCA-2018-10-3-359

Abstract

(1) Let $R$ be a commutative Noetherian ring of dimension $n$ and $P$ a projective $R[X_1,\ldots ,X_m]$-module of rank $n$. In this paper, we associate an obstruction for $P$ to split off a free summand of rank one. (2) Let $R$ be a local ring and $R[X]\subset A\subset R[X,X^{-1}]$. Let $P$ and $Q$ be two projective $A$-modules with $\text {rank}(Q)\lt \text {rank}(P)$. If $Q_f$ is a direct summand of $P_f$ for some special monic polynomial $f\in R[X]$, then $Q$ is also a direct summand of $P$.

Citation

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Manoj K. Keshari and Md. Ali Zinna. "Unimodular elements in projective modules and an analogue of a result of Mandal." J. Commut. Algebra 10 (3) 359 - 373, 2018. https://doi.org/10.1216/JCA-2018-10-3-359

Information

Published: 2018
First available in Project Euclid: 9 November 2018

zbMATH: 06976321
MathSciNet: MR3874658
Digital Object Identifier: 10.1216/JCA-2018-10-3-359

Subjects:
Primary: 13C10

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.10 • No. 3 • 2018
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