On the torsion theories of Morita equivalent rings
type: Item
instance of: scholarly article
title: On the torsion theories of Morita equivalent rings
zbMATH Open document ID: 0859.16023
DOI: 10.1007/BF02109788
published in: Periodica Mathematica Hungarica
publication date: 1997-04-13T00:00:00Z
review text: Let \(R\) and \(S\) be Morita equivalent rings, and let \(W\) be a bimodule that gives the equivalence of categories: \(\alpha=W\otimes_R-:R\text{-mod}\to S\text{-mod}\). Let \(0\to R\to E_0\to E_1\to\cdots\) be a minimal injective resolution of \(R\), and let \(\sigma_n\) be the torsion theory cogenerated by \(E_0\oplus E_1\oplus\cdots\oplus E_n\). Let \(\tau_n\) be a torsion theory defined in a similar way by a minimal injective resolution of \(S\). Then \(\alpha(\sigma_n(R))=\tau_n(S)\), and hence the localizations \(R_{\sigma_n}\) and \(S_{\tau_n}\) are Morita equivalent. This paper also examines the effect of \(\alpha\) on properties of some other torsion theories, especially the Goldie torsion theory.
Mathematics Subject Classification ID: 16S90
Mathematics Subject Classification ID: 16D90
zbMATH DE Number: 938668
zbMATH Keywords: Morita equivalent rings
zbMATH Keywords: equivalence of categories
zbMATH Keywords: injective resolutions
zbMATH Keywords: localizations
zbMATH Keywords: Goldie torsion theory
author: Ahmad Haghany
reviewed by: Mark L. Teply
MaRDI profile type: Publication
cites work: Q4055809
cites work: Q4849467
cites work: Q4132671
cites work: Q3786586
cites work: The quotient category of a Morita context
cites work: An alternate criterion of localized modules
cites work: Morita context functors
full work available at URL: https://doi.org/10.1007/bf02109788
OpenAlex ID: W2074802003
description: scientific article; zbMATH DE number 938668