When every projective module is a direct sum of finitely generated modules

Gennady Puninskiy; Warren Wm McGovern; Gena Puninski; Philipp Rothmaler

doi:10.1016/j.jalgebra.2007.01.043

When every projective module is a direct sum of finitely generated modules

Gennady Puninskiy, Warren Wm McGovern, Gena Puninski, Philipp Rothmaler

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

Abstract

We characterize rings over which every projective module is a direct sum of finitely generated modules, and give various examples of rings with and without this property. © 2007 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	454-481
Number of pages	27
Journal	Journal of Algebra
Volume	315
Issue number	1
DOIs	https://doi.org/10.1016/j.jalgebra.2007.01.043
Publication status	Published - 1 Sep 2007

Keywords

(Weakly) semihereditary ring
Bézout ring
Decomposition theory
Non-finitely generated projective module
Principal ideal ring
Rings of continuous functions

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10.1016/j.jalgebra.2007.01.043

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title = "When every projective module is a direct sum of finitely generated modules",

abstract = "We characterize rings over which every projective module is a direct sum of finitely generated modules, and give various examples of rings with and without this property. {\textcopyright} 2007 Elsevier Inc. All rights reserved.",

keywords = "(Weakly) semihereditary ring, B{\'e}zout ring, Decomposition theory, Non-finitely generated projective module, Principal ideal ring, Rings of continuous functions",

author = "Gennady Puninskiy and McGovern, {Warren Wm} and Gena Puninski and Philipp Rothmaler",

year = "2007",

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AU - Puninskiy, Gennady

AU - McGovern, Warren Wm

AU - Puninski, Gena

AU - Rothmaler, Philipp

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N2 - We characterize rings over which every projective module is a direct sum of finitely generated modules, and give various examples of rings with and without this property. © 2007 Elsevier Inc. All rights reserved.

AB - We characterize rings over which every projective module is a direct sum of finitely generated modules, and give various examples of rings with and without this property. © 2007 Elsevier Inc. All rights reserved.

KW - (Weakly) semihereditary ring

KW - Bézout ring

KW - Decomposition theory

KW - Non-finitely generated projective module

KW - Principal ideal ring

KW - Rings of continuous functions

U2 - 10.1016/j.jalgebra.2007.01.043

DO - 10.1016/j.jalgebra.2007.01.043

M3 - Article

VL - 315

SP - 454

EP - 481

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 1

ER -

When every projective module is a direct sum of finitely generated modules

Abstract

Keywords

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