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GORENSTEIN DIMENSIONS MODULO A REGULAR ELEMENT

Part of: Homological algebra Commutative algebra: Homological methods

Published online by Cambridge University Press:  03 June 2015

SHAHAB RAJABI  and
SIAMAK YASSEMI
SHAHAB RAJABI*
Affiliation:
School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran email shahabrjb@gmail.com
SIAMAK YASSEMI
Affiliation:
School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran email yassemi@ut.ac.ir
*
✉shahabrjb@ipm.ir
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Abstract

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Let $R$ be a commutative ring. In this paper we study the behavior of Gorenstein homological dimensions of a homologically bounded $R$-complex under special base changes to the rings $R_{x}$ and $R/xR$, where $x$ is a regular element in $R$. Our main results refine some known formulae for the classical homological dimensions. In particular, we provide the Gorenstein counterpart of a criterion for projectivity of finitely generated modules, due to Vasconcelos.

Keywords

Gorenstein homological dimensionderived category

MSC classification

Primary: 13D05: Homological dimension
Secondary: 18G20: Homological dimension 18G25: Relative homological algebra, projective classes 18G35: Chain complexes
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 99 , Issue 2 , October 2015 , pp. 260 - 266
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

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