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Weak dimensions and Gorenstein weak dimensions of group rings. (English) Zbl 07396198

Summary: Let \(K\) be a field, and let \(G\) be a group. In the present paper, we investigate when the group ring \(K[G]\) has finite weak dimension and finite Gorenstein weak dimension. We give some analogous versions of Serre’s theorem for the weak dimension and the Gorenstein weak dimension.

MSC:

16S34 Group rings
16E10 Homological dimension in associative algebras
16E30 Homological functors on modules (Tor, Ext, etc.) in associative algebras
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