Separable ring extensions and cohomological dimension
type: Item
instance of: scholarly article
title: Separable ring extensions and cohomological dimension
zbMATH Open document ID: 0647.16017
DOI: 10.1016/0021-8693(88)90112-3
author: Aboubakr Lbekkouri
published in: Journal of Algebra
publication date: 1988-01-01T00:00:00Z
review text: The author introduces the notion of separable K-rings to generalize several results on cohomological dimension of algebras due to \textit{M. Auslander} [Nagoya Math. J. 9, 67-77 (1955; Zbl 0067.271) and ibid. 11, 61-65 (1957; Zbl 0212.058)], \textit{S. Eilenberg}, \textit{M. Ikeda} and \textit{T. Nakayama} [Nagoya Math. J. 8, 49-57 (1955; Zbl 0066.288) and Comment. Math. Helv. 28, 310-319 (1954; Zbl 0058.028)] and others. It is proved that the cohomological dimension of a semiprimary purely inseparable algebra over a field is infinite. Furthermore, a relative version of one inequality for projective and cohomological dimensions by \textit{G. Hochschild} [Nagoya Math. J. 13, 89-94 (1958; Zbl 0085.266)] is given.
Mathematics Subject Classification ID: 16E10
Mathematics Subject Classification ID: 16Exx
Mathematics Subject Classification ID: 16H05
Mathematics Subject Classification ID: 18G20
Mathematics Subject Classification ID: 18G25
zbMATH DE Number: 4055815
zbMATH Keywords: projective dimensions
zbMATH Keywords: relatively projective resolution
zbMATH Keywords: separable K- rings
zbMATH Keywords: cohomological dimension of algebras
reviewed by: Marek Golasiński
MaRDI profile type: Publication
full work available at URL: 0021-8693(88)90112-3
OpenAlex ID: W2060969174
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description: scientific article; zbMATH DE number 4055815