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CARTAN–EILENBERG FP-INJECTIVE COMPLEXES

Part of: Homological algebra

Published online by Cambridge University Press:  23 December 2016

BO LU  and
ZHONGKUI LIU
BO LU*
Affiliation:
College of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou 730030, Gansu, PR China email lubo55@126.com
ZHONGKUI LIU
Affiliation:
Department of Mathematics, Northwest Normal University, Lanzhou 730070, Gansu, PR China email liuzk@nwnu.edu.cn
*
✉lubo55@126.com
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Abstract

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In this article, we extend the notion of FP-injective modules to that of Cartan–Eilenberg complexes. We show that a complex $C$ is Cartan–Eilenberg FP-injective if and only if $C$ and $\text{Z}(C)$ are complexes consisting of FP-injective modules over right coherent rings. As an application, coherent rings are characterized in various ways, using Cartan–Eilenberg FP-injective and Cartan–Eilenberg flat complexes.

Keywords

Cartan–Eilenberg FP-injective complexCartan–Eilenberg flat complexcoherent ring

MSC classification

Primary: 18G35: Chain complexes
Secondary: 18G15: Ext and Tor, generalizations, Künneth formula
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 103 , Issue 3 , December 2017 , pp. 387 - 401
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

Footnotes

This research was supported by the National Natural Science Foundation of China (No. 11501451), the Fundamental Research Funds for the Central Universities (No. 31920150038) and XBMUYJRC (No. 201406).

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