On the finiteness of the global dimension for artinian rings

Andrzej Skowroński; Sverre O. Smalo; Dan Zacharia

doi:10.1006/jabr.2001.9130

On the finiteness of the global dimension for artinian rings

Andrzej Skowroński, Sverre O. Smalo, Dan Zacharia

Department of Mathematics

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

2 Scopus citations

Abstract

In this note we prove that for a left artinian ring of infinite global dimension there exists an indecomposable left module with both infinite projective dimension and infinite injective dimension.

Original language	English (US)
Pages (from-to)	475-478
Number of pages	4
Journal	Journal of Algebra
Volume	251
Issue number	1
DOIs	https://doi.org/10.1006/jabr.2001.9130
State	Published - May 1 2002

ASJC Scopus subject areas

Algebra and Number Theory

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10.1006/jabr.2001.9130

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title = "On the finiteness of the global dimension for artinian rings",

abstract = "In this note we prove that for a left artinian ring of infinite global dimension there exists an indecomposable left module with both infinite projective dimension and infinite injective dimension.",

author = "Andrzej Skowro{\'n}ski and Smalo, {Sverre O.} and Dan Zacharia",

note = "Funding Information: 1Supported by Polish Scientific Grant KBN 5P03A00821 and the Foundation for Polish Science. 2Supported by the Research Council of Norway.",

year = "2002",

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doi = "10.1006/jabr.2001.9130",

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T1 - On the finiteness of the global dimension for artinian rings

AU - Skowroński, Andrzej

AU - Smalo, Sverre O.

AU - Zacharia, Dan

N1 - Funding Information: 1Supported by Polish Scientific Grant KBN 5P03A00821 and the Foundation for Polish Science. 2Supported by the Research Council of Norway.

PY - 2002/5/1

Y1 - 2002/5/1

N2 - In this note we prove that for a left artinian ring of infinite global dimension there exists an indecomposable left module with both infinite projective dimension and infinite injective dimension.

AB - In this note we prove that for a left artinian ring of infinite global dimension there exists an indecomposable left module with both infinite projective dimension and infinite injective dimension.

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U2 - 10.1006/jabr.2001.9130

DO - 10.1006/jabr.2001.9130

M3 - Article

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VL - 251

SP - 475

EP - 478

JO - Journal of Algebra

JF - Journal of Algebra

IS - 1

ER -

On the finiteness of the global dimension for artinian rings

Abstract

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