Interdisciplinary Information Sciences
Online ISSN : 1347-6157
Print ISSN : 1340-9050
ISSN-L : 1340-9050
Special Section: Japan-Korea Joint Seminar on Number Theory and Related Topics 2008
Flat Modules and Gröbner Bases over Truncated Discrete Valuation Rings
Toshiro HIRANOUCHI, Yuichiro TAGUCHI
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Keywords: Gröbner bases, flat modules, truncated discrete valuations ring
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2010 Volume 16 Issue 1 Pages 33-37

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Abstract
We present basic properties of Gröbner bases of submodules of a free module of finite rank over a polynomial ring R with coefficients in a graded truncated discrete valuations ring A. As an application, we give a criterion for a finitely generated R-module to be flat over A. Its non-graded version is also given.
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© 2010 by the Graduate School of Information Sciences (GSIS), Tohoku University

This article is licensed under a Creative Commons [Attribution 4.0 International] license.
https://creativecommons.org/licenses/by/4.0/
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