The Anick resolution
type: Item
instance of: scholarly article
title: The Anick resolution
zbMATH Open document ID: 0798.16012
DOI: 10.1016/0022-4049(92)90155-9
author: Daniel R. Farkas
published in: Journal of Pure and Applied Algebra
publication date: 1993-01-16T00:00:00Z
review text: \textit{D. J. Anick} [Trans. Am. Math. Soc. 269, 641-659 (1986; Zbl 0598.16028)] constructs a free resolution of a field \(k\) over any algebra presented by the free algebra \(k\{X_ 1,\dots,X_ n\}\) with relations in the augmentation ideal. The author shows that the maps in that resolution have an explicit decomposition using the tools of noncommutative Gröbner bases theory [\textit{F. Mora}, Proc. 3rd Int. Conf., Grenoble/France 1985, Lect. Notes Comput. Sci. 229, 353-363 (1986; Zbl 0659.16003)]. An evidence of that has been found by \textit{E. L. Green} et al. [Commun. Algebra 21, No. 6, 1869-1887 (1993; Zbl 0796.16006)].
Mathematics Subject Classification ID: 16S10
Mathematics Subject Classification ID: 18G10
Mathematics Subject Classification ID: 16E60
Mathematics Subject Classification ID: 16E30
zbMATH DE Number: 89567
zbMATH Keywords: free resolutions
zbMATH Keywords: free algebras
zbMATH Keywords: relations
zbMATH Keywords: augmentation ideal
zbMATH Keywords: noncommutative Gröbner bases
reviewed by: Marek Golasiński
MaRDI profile type: Publication
full work available at URL: 0022-4049(92)90155-9
OpenAlex ID: W2065947085
cites work: On the Homology of Associative Algebras
cites work: Do subspaces have distinguished bases?
cites work: Constructing projective resolutions
Recommended article: The Buchberger resolution
Recommended article: An analogical approach of resolution
Recommended article: Q4938528
Recommended article: Auslander-Gorenstein resolution.
Recommended article: ANR-resolutions of triads
Recommended article: An addendum to bo-resolutions
Recommended article: Q4302462
Recommended article: The intractability of resolution
Recommended article: Resolving a question of Arkhangel'skiĭ's
Recommended article: Bezoutians and Tate resolutions
description: scientific article; zbMATH DE number 89567