We study the properties of rings satisfying Auslander-type conditions. If an artin algebra Λ satisfies the Auslander condition (that is, Λ is an ∞-Gorenstein artin algebra), then we construct two kinds of subcategories which form functorially finite cotorsion theories. Noetherian rings satisfying ‘Auslander-type conditions’ on self-injective resolutions can be regarded as certain non-commutativ...

The formulation of global health policy is political; and all institutions operating in the global health landscape are political. This is because policies and institutions inevitably represent certain values, reflect particular ideologies, and preferentially serve some interests over others. This may be expressed explicitly and consciously; or implicitly and unconsciously. But it’s important t...

We introduce the notion of a duality pair and demonstrate how the left half of such a pair is “often” covering and preenveloping. As an application, we generalize a result by Enochs et al. on Auslander and Bass classes, and we prove that the class of Gorenstein injective modules—introduced by Enochs and Jenda—is covering when the ground ring has a dualizing complex.

We prove that the Auslander class determined by a semidualizing module is the left half of a perfect cotorsion pair. We also prove that the Bass class determined by a semidualizing module is preenveloping. 0. Introduction The notion of semidualizing modules over commutative noetherian rings goes back to Foxby [11] and Golod [13]. Christensen [3] extended this notion to semidualizing complexes. ...

We present a classification of those finite length modules X over a ring A which are isomorphic to every module Y of the same length such that Ker(HomA(−, X)) = Ker(HomA(−, Y )), i.e. X is determined by its length and the torsion pair cogenerated by X. We also prove the dual result using the torsion pair generated by X. For A right hereditary, we prove an analogous classification using the coto...

Falling long-term interest rates worldwide have led some policy-makers to speculate on the emergence of a glut of global saving (Bernanke, 2005). The global trend contrasts markedly with that of the United States, where the public discussion has focused on an ongoing decline of private saving and the re-emergence of large budget deficits. The absence of saving in the United States, in conjuncti...

Let G be an associative monomial k-algebra. If G is assumed to be finitely presented, then either G contains a free subalgebra on two monomials or else G has polynomial growth. If instead G is assumed to have finite global dimension, then either G contains a free subalgebra or else G has a finite presentation and polynomial growth. Also, a graded Hopf algebra with generators in degree one and r...

In this paper, we prove that the global Gorenstein projective dimension of a ring R is equal to the global Gorenstein injective dimension of R, and that the global Gorenstein flat dimension of R is smaller than the common value of the terms of this equality.

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