ACTA MATHEMATICA
UNIVERSITATIS COMENIANAE




On (weak) Gorenstein global dimensions

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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Acta Mathematica Universitatis Comenianae
ISSN 0862-9544   (Printed edition)

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