Gorenstein homomorphisms of noncommutative rings
type: Item
instance of: scholarly article
title: Gorenstein homomorphisms of noncommutative rings
zbMATH Open document ID: 0926.16036
author: Peter Jørgensen
published in: Journal of Algebra
publication date: 1999-11-30T00:00:00Z
review text: Let \(k\) be a field, \(R\) and \(S\) connected graded Noetherian \(k\)-algebras with balanced dualizing complexes. Let \(\rho\colon R\to S\) be a graded algebra homomorphism such that \(S\) has finite flat dimension as both a left and right \(R\)-module. Then the definition of a Gorenstein homomorphism is given for such a \(\rho\), and a theory for such homomorphisms is developed. ``Ascent-descent'' and ``Base-change'' results are proven, and generalizations of some classical results on Gorenstein algebras are obtained.
Mathematics Subject Classification ID: 16W50
Mathematics Subject Classification ID: 16E65
Mathematics Subject Classification ID: 16E05
Mathematics Subject Classification ID: 16W20
Mathematics Subject Classification ID: 13H10
zbMATH DE Number: 1251303
zbMATH Keywords: connected graded Noetherian algebras
zbMATH Keywords: balanced dualizing complexes
zbMATH Keywords: graded algebra homomorphisms
zbMATH Keywords: flat dimension
zbMATH Keywords: Gorenstein homomorphisms
zbMATH Keywords: Gorenstein algebras
reviewed by: Serban Raianu
MaRDI profile type: Publication
full work available at URL: jabr.1998.7608
OpenAlex ID: W2066822757
cites work: Noncommutative projective schemes
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DOI: 10.1006/JABR.1998.7608
description: scientific article; zbMATH DE number 1251303