Global Gorenstein dimensions of polynomial rings and of direct products of rings

Abstract

In this paper, we extend the well-known Hilbert's syzygy theorem to the Gorenstein homological dimensions of rings. Also, we study the Gorenstein homological dimensions of direct products of rings. Our results generate examples of non-Noetherian rings of finite Gorenstein dimensions and infinite classical weak dimension.

Cited by in corpus (6)

• Super finitely presented modules and Gorenstein projective modules
• Note on (weak) Gorenstein global dimensions
• When an amalgamated duplication of a ring along an ideal is quasi-Frobenius
• Gorenstein global dimension of an amalgamated duplication of a coherent ring along an ideal
• $n$-strongly Gorenstein rings
• Self injective property in amalgamated algebra along an ideal