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Some Homological Criteria for Regular, Complete Intersection and Gorenstein Rings

Part of: Commutative algebra: Homological methods Local rings and semilocal rings

Published online by Cambridge University Press:  08 July 2015

Javier Majadas
Javier Majadas*
Affiliation:
Departamento de Álgebra, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15782 Santiago de Compostela, Spain, ([email protected])
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Abstract

Regularity, complete intersection and Gorenstein properties of a local ring can be characterized by homological conditions on the canonical homomorphism into its residue field. In positive characteristic, the Frobenius endomorphism (and, more generally, any contracting endomorphism) can also be used for these characterizations. We introduce here a class of local homomorphisms, in some sense larger than all above, for which these characterizations still hold, providing an unified treatment for this class of homomorphisms.

Keywords

regular local ringfinite flat dimensioncomplete intersection

MSC classification

Primary: 13H05: Regular local rings 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
Secondary: 13D03: (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.) 13D05: Homological dimension
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 2 , May 2016 , pp. 473 - 481
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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