Relative transpose and its dual with respect to a bimodule
type: Item
instance of: scholarly article
title: Relative transpose and its dual with respect to a bimodule
zbMATH Open document ID: 1395.18014
author: Guoqiang Zhao
published in: Algebras and Representation Theory
publication date: 2018-02-15T00:00:00Z
review text: Given a class \(\mathcal{X}\) of modules, the author introduces the notion of \(\mathcal{X}\)-transposes of modules with respect to a bimodule in the present paper, which unifies some well-known notions of transposes, such as Auslander transposes, Gorenstein transposes, \(C\)-Gorenstein transposes and so on. Several known results are extended, and for a subclass \(\mathcal{V}\) of \(\mathcal{X}\), some relations between \(\mathcal{X}\)-transposes and \(\mathcal{V}\)-transposes are established. The dual aspects of \(\mathcal{X}\)-transposes are also discussed in the paper. That is, the author introduces \(\mathcal{X}\)-cotransposes of modules with respect to a bimodule. In particular, the dual counterparts of Gorenstein transposes are established.
reviewed by: Li Liang
Mathematics Subject Classification ID: 18G25
Mathematics Subject Classification ID: 18G10
zbMATH DE Number: 6839342
zbMATH Keywords: \(\mathcal{X}\)-transpose
zbMATH Keywords: semidualizing bimodule
zbMATH Keywords: Gorenstein module
zbMATH Keywords: Bass class
zbMATH Keywords: Y-cotranspose
zbMATH Keywords: Gorenstein (co)transpose
MaRDI profile type: Publication
full work available at URL: s10468-017-9708-x
OpenAlex ID: W2627014905
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DOI: 10.1007/S10468-017-9708-X
description: scientific article; zbMATH DE number 6839342