Cyclic homology of monogenic extensions
type: Item
instance of: scholarly article
title: Cyclic homology of monogenic extensions
zbMATH Open document ID: 0703.13013
DOI: 10.1016/0022-4049(90)90030-L
author: Jorge Alberto Cuccione
author: Juan José Cuccione
published in: Journal of Pure and Applied Algebra
publication date: 1990-01-01T00:00:00Z
review text: Let D be a commutative k-algebra and S a multiplicative subset of k[X]. After defining mixed complexes and strongly homotopy k-maps, the authors prove that for \(A=k[X]/<X^ n>\), where k is a commutative ring with identity, the double complex \(B(A)_{norm}\) defined by Loday and Quillen can be replaced by an easier complex. This leads to a computation of the cyclic homology of \(D[X]/<X^ n>\) and \(S^{-1}D[X]\) in terms of the cyclic and Hochschild homology of D, where D is a k-algebra with k a commutative ring containing a field. Similar results are obtained for cohomology. Finally, when k is a field, the authors compute the cyclic homology and cohomology of D[X \(]/ \), with P a polynomial in k[X]. These results are obtained without assuming characteristic zero.
Mathematics Subject Classification ID: 13D03
Mathematics Subject Classification ID: 13D25
zbMATH DE Number: 4152542
zbMATH Keywords: monogenic extensions
zbMATH Keywords: Loday Quillen complex
zbMATH Keywords: cyclic homology
zbMATH Keywords: Hochschild homology
reviewed by: T. W. Hungerford
MaRDI profile type: Publication
cites work: The Künneth formula in cyclic homology
cites work: Cyclic homology, comodules, and mixed complexes
cites work: Cyclic homology and the Lie algebra homology of matrices
cites work: Cyclic cohomology of \(A[X]\) and \(A[X,X^{-1}]\)
cites work: Nil K-Theory Maps to Cyclic Homology
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description: scientific article; zbMATH DE number 4152542