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On (weak) Gorenstein global dimensions

Author(s): N. Mahdou | M. Tamekkante

Journal: Acta Mathematica Universitatis Comenianae
ISSN 0862-9544

Volume: LXXXII;
Issue: 2;
Start page: 285;
Date: 2013;
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Keywords: weak (Gorenstein) homological dimensions | Hilbert's syzygy Theorem

In this note, we characterize the (weak) Gorenstein global dimension for arbitrary associative rings. Also, we extend the well-known Hilbert's syzygy Theorem to the weak Gorenstein global dimension, and we study the weak Gorenstein homological dimensions of direct product of rings which gives examples of non-coherent rings with finite Gorenstein dimensions > 0 and infinite classical weak dimension.
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