On the $ C $-flatness and injectivity of character modules

Zhaoyong Huang; Zhaoyong Huang

doi:10.3934/era.2022147

Electronic Research Archive

2022, Volume 30, Issue 8: 2899-2910. doi: 10.3934/era.2022147

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Research article

On the $ C $-flatness and injectivity of character modules

Zhaoyong Huang ^,

Department of Mathematics, Nanjing University, Nanjing 210093, China

Received: 24 October 2021 Revised: 28 March 2022 Accepted: 19 April 2022 Published: 30 May 2022

Let $ R, S $ be arbitrary associative rings and $ _RC_S $ 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 $-($ {\mathop{{{\text{FP}}}}\nolimits} $-)injectivity, flatness and projectivity of character modules of certain left $ S $-modules.
Citation: Zhaoyong Huang. On the $ C $-flatness and injectivity of character modules[J]. Electronic Research Archive, 2022, 30(8): 2899-2910. doi: 10.3934/era.2022147

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Abstract

Let $ R, S $ be arbitrary associative rings and $ _RC_S $ 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 $-($ {\mathop{{{\text{FP}}}}\nolimits} $-)injectivity, flatness and projectivity of character modules of certain left $ S $-modules.

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