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Benson's cofibrants, Gorenstein projectives and a related conjecture

Part of: Homological algebra Theory of modules and ideals Commutative algebra: Homological methods

Published online by Cambridge University Press:  23 September 2021

Rudradip Biswas
Rudradip Biswas*
Affiliation:
Department of Mathematics, University of Manchester, Oxford Road, ManchesterM13 9PL, UK ([email protected])
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Abstract

In this short article, we will be principally investigating two classes of modules over any given group ring – the class of Gorenstein projectives and the class of Benson's cofibrants. We begin by studying various properties of these two classes and studying some of these properties comparatively against each other. There is a conjecture made by Fotini Dembegioti and Olympia Talelli that these two classes should coincide over the integral group ring for any group. We make this conjecture over group rings over commutative rings of finite global dimension and prove it for some classes of groups while also proving other related results involving the two classes of modules mentioned.

Keywords

Benson's cofibrantsGorenstein projectivesKropholler's hierarchycomplete resolutions

MSC classification

Primary: 18G05: Projectives and injectives 13C10: Projective and free modules and ideals 13C60: Module categories
Secondary: 13D02: Syzygies, resolutions, complexes
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 64 , Issue 4 , November 2021 , pp. 779 - 799
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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