This dissertation presents a homological dimension notion of Cohen-Macaulay for non-
Noetherian rings which reduces to the standard definition in the case that the ring is …

In Noetherian rings there is a hierarchy among regular, Gorenstein and Cohen-Macaulay
rings. Regular non-Noetherian rings were originally defined by Bertin in 1971. In 2007 …

Theories of coherent Cohen–Macaulay and Gorenstein rings have recently been developed
by Hamilton and Marley, and Hummel and Marley, respectively. This work summarizes these …

In this paper, we define a homological invariant for finitely generated modules over a
commutative noetherian local ring. which we call upper Cohen-Macaulay dirnension. This …

Commutative ring theory is a branch of algebra which was born in the late 19th century. In
the 1870s, JWR Dedekind introduced the notion of an ideal in his research of the rings of …

A new homological dimension, called GCM-dimension, will be defined for any finitely
generated module M over a local Noetherian ring R. GCM-dimension (short for Generalized …

We introduce new homological dimensions, namely the Cohen-Macaulay projective,
injective and flat dimensions for homologically bounded complexes. Among other things we …

In this paper, we define a homological invariant for finitely generated modules over a
commutative noetherian local ring, which we call upper Cohen-Macaulay dimension. This …

In this paper we use" ring changed''Gorenstein homological dimensions to define Cohen-
Macaulay injective, projective and flat dimensions. For doing this we use the amalgamated …

Let (R, m) be commutative Noetherian local ring. It is shown that R is Cohen-Macaulay ring if
there exists a Cohen-Macaulay finite (ie finitely generated) R-module with finite upper …