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Research Article | Open Access

On the C-flatness and injectivity of character modules

Department of Mathematics, Nanjing University, Nanjing 210093, China
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Abstract

Let R,S be arbitrary associative rings and RCS a semidualizing bimodule. We give some equivalent characterizations for R being left coherent (and right perfect) rings, left Noetherian rings and left Artinian rings in terms of the C-( FP-)injectivity, flatness and projectivity of character modules of certain left S-modules.

Keywords

character modulesC-flatnessC-projectivityC-(FP-)injectivityleft coherent (and right perfect) ringsleft Noetherian ringsleft Artinian rings

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Electronic Research Archive
Volume 30 Issue 8,
August 2022
Pages 2899-2910
DOI: 10.3934/era.2022147

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Cite this article:
Huang Z. On the C-flatness and injectivity of character modules. Electronic Research Archive, 2022, 30(8): 2899-2910. https://doi.org/10.3934/era.2022147

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Received: 24 October 2021
Revised: 28 March 2022
Accepted: 19 April 2022
Published: 15 August 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)