N. Mahdou and M. Tamekkante
Received: January 14, 2013; Accepted: March 3, 2013
Abstract. 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.
Keywords: weak (Gorenstein) homological dimensions; Hilbert's syzygy Theorem.
AMS Subject classification: Primary: 13D05, 13D02
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