On projective modules over polynomial rings

Moshe Roitman

doi:10.1016/0021-8693(79)90188-1

On projective modules over polynomial rings

Research output: Contribution to journal › Article › peer-review

Abstract

We prove here, among other results, that if R is a commutative noetherian ring and projective R[x₁, ..., x_n]-modules of rank ≤ Krull dim R are extended, then finitely generated projective R[x₁, ..., x_n]-modules are extended. We also give an example of a nonfinitely generated projective module over an integral domain which contains no unimodular elements.

Original language	English
Pages (from-to)	51-63
Number of pages	13
Journal	Journal of Algebra
Volume	58
Issue number	1
DOIs	https://doi.org/10.1016/0021-8693(79)90188-1
State	Published - May 1979
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/0021-8693(79)90188-1

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title = "On projective modules over polynomial rings",

abstract = "We prove here, among other results, that if R is a commutative noetherian ring and projective R[x1, ..., xn]-modules of rank ≤ Krull dim R are extended, then finitely generated projective R[x1, ..., xn]-modules are extended. We also give an example of a nonfinitely generated projective module over an integral domain which contains no unimodular elements.",

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AB - We prove here, among other results, that if R is a commutative noetherian ring and projective R[x1, ..., xn]-modules of rank ≤ Krull dim R are extended, then finitely generated projective R[x1, ..., xn]-modules are extended. We also give an example of a nonfinitely generated projective module over an integral domain which contains no unimodular elements.

UR - https://www.scopus.com/pages/publications/0040075698

U2 - 10.1016/0021-8693(79)90188-1

DO - 10.1016/0021-8693(79)90188-1

M3 - Article

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VL - 58

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JO - Journal of Algebra

JF - Journal of Algebra

IS - 1

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On projective modules over polynomial rings

Abstract

ASJC Scopus subject areas

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