Global Dimension of Differential Operator Rings

Rings with Finite Gorenstein Global Dimension

We find new classes of non noetherian rings which have the same homological behavior that Gorenstein rings.

Differential Polynomial Rings of Triangular Matrix Rings

On co-Noetherian dimension of rings

We define and studyco-Noetherian dimension of rings for which the injective envelopeof simple modules have finite Krull-dimension. This  is a Moritainvariant dimension that measures how far the ring is from beingco-Noetherian. The co-Noetherian dimension of certain rings,including commutative rings, are determined. It is shown that the class ${mathcal W}_n$ of rings with co-Noetherian dimension...

Global Dimension of Polynomial Rings in Partially Commuting Variables

For any free partially commutative monoid M(E, I), we compute the global dimension of the category of M(E, I)-objects in an Abelian category with exact coproducts. As a corollary, we generalize Hilbert’s Syzygy Theorem to polynomial rings in partially commuting variables.

Gorenstein Global Dimensions and Cotorsion Dimension of Rings

In this paper, we establish, as a generalization of a result on the classical homological dimensions of commutative rings, an upper bound on the Gorenstein global dimension of commutative rings using the global cotorsion dimension of rings. We use this result to compute the Gorenstein global dimension of some particular cases of trivial extensions of rings and of group rings.