Some results on Gorenstein (weak) global dimension of rings

Abstract

The principle “Every result in classical homological algebra should have a counterpart in Gorenstein homological algebra” was given by Henrik Holm. We give support to the principle. We prove that the Gorenstein weak global dimension of a ring R equals the supremum of the Gorenstein flat dimensions of the finitely presented cyclic (left or right) R-modules. We also show that, if R is a coherent ring and x is a central nonzero-divisor in R contained in the Jacobson radical of R, then Finally, we give the Gorenstein counterpart of the well-known Hilbert’s Syzygy Theorem.