Note on (weak) Gorenstein global dimensions

Details Note on (weak) Gorenstein global dimensions Note on (weak) Gorenstein global dimensions

2009-10-29

arxiv.org/abs/0910.5752v1

Mathematics

Commutative Algebra

Scientific paper

In this note we characterize the (resp., weak) Gorenstein global dimension for an arbitrary ring. 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 of finite Gorenstein dimensions $>0$ and infinite classical weak dimension.

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