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Let be a left and right Noetherian ring and a semidualizing -bimodule. We introduce a transpose of an -module with respect to which unifies the Auslander transpose and Huang’s transpose, see Z. Y. Huang, On a generalization of the Auslander-Bridger transpose, Comm. Algebra 27 (1999), 5791–5812, in the two-sided Noetherian setting, and use to develop further the generalized Gorenstein dimension with respect to . Especially, we generalize the Auslander-Bridger formula to the generalized...
We provide a characterization of artin algebras without chains of nonzero homomorphisms between indecomposable finitely generated modules starting with an injective module and ending with a projective module.
This text gives a short overview of the recent works on Gorenstein global dimension of rings.
This paper discusses a variant theory for the Gorenstein flat dimension. Actually, since it is not yet known whether the category (R) of Gorenstein flat modules over a ring R is projectively resolving or not, it appears legitimate to seek alternate ways of measuring the Gorenstein flat dimension of modules which coincide with the usual one in the case where (R) is projectively resolving, on the one hand, and present nice behavior for an arbitrary ring R, on the other. In this paper, we introduce...
The aim of this work is to characterize the algebras which are standardly stratified with respect to any order of the simple modules. We show that such algebras are exactly the algebras with all idempotent ideals projective. We also deduce as a corollary a characterization of hereditary algebras, originally due to Dlab and Ringel.
Let m ≥ 2 be an integer. By using m submodules of a given module, we construct a certain exact sequence, which is a well known short exact sequence when m = 2. As an application, we compute a minimal projective resolution of the Jacobson radical of a tiled order.
Let G be a group, R a G-graded ring and X a right G-set. We study functors between categories of modules graded by G-sets, continuing the work of [M]. As an application we obtain generalizations of Cohen-Montgomery Duality Theorems by categorical methods. Then we study when some functors introduced in [M] (which generalize some functors ocurring in [D1], [D2] and [NRV]) are separable. Finally we obtain an application to the study of the weak dimension of a group graded ring.
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