An artin algebra A over a commutative artin ring R is called quasitilted if gl.dim A ≤ 2 and for each indecomposable finitely generated A-module M we have pd M ≤ 1 or id M ≤ 1. In [11] several characterizations of quasitilted algebras were proven. We investigate the structure and homological properties of connected components in the Auslander-Reiten quiver of a quasitilted algebra A.
In this paper, we use a characterization of -modules such that to characterize Cohen-Macaulay rings in terms of various dimensions. This is done by setting to be the local cohomology functor of with respect to the maximal ideal where is the Krull dimension of .
Let be a commutative Noetherian ring and let be a semidualizing -module. We prove a result about the covering properties of the class of relative Gorenstein injective modules with respect to which is a generalization of Theorem 1 by Enochs and Iacob (2015). Specifically, we prove that if for every -injective module , the character module is -flat, then the class is closed under direct sums and direct limits. Also, it is proved that under the above hypotheses the class is covering....
In this paper, we study some properties of -flat -modules, where is a semidualizing module over a commutative ring and we investigate the relation between the -yoke with the -yoke of a module as well as the relation between the -flat resolution and the flat resolution of a module over -closed rings. We also obtain a criterion for computing the -flat dimension of modules.
Let be a self-orthogonal class of left -modules. We introduce a class of modules, which is called strongly -Gorenstein modules, and give some equivalent characterizations of them. Many important classes of modules are included in these modules. It is proved that the class of strongly -Gorenstein modules is closed under finite direct sums. We also give some sufficient conditions under which the property of strongly -Gorenstein module can be inherited by its submodules and quotient modules....
We show that the dimension of the derived category of an elliptic curve or a tubular weighted projective line is one. We give explicit generators realizing this number, and show that they are in a certain sense minimal.