Displaying similar documents to “Stable Clifford theory for divisorially graded rings.”

Weak Baer modules over graded rings

Mark Teply, Blas Torrecillas (1998)

Colloquium Mathematicae


In [2], Fuchs and Viljoen introduced and classified the B * -modules for a valuation ring R: an R-module M is a B * -module if E x t R 1 ( M , X ) = 0 for each divisible module X and each torsion module X with bounded order. The concept of a B * -module was extended to the setting of a torsion theory over an associative ring in [14]. In the present paper, we use categorical methods to investigate the B * -modules for a group graded ring. Our most complete result (Theorem 4.10) characterizes B * -modules for a strongly graded...

Strongly graded left FTF rings.

José Gómez, Blas Torrecillas (1992)

Publicacions Matemàtiques


An associated ring R with identity is said to be a left FTF ring when the class of the submodules of flat left R-modules is closed under injective hulls and direct products. We prove (Theorem 3.5) that a strongly graded ring R by a locally finite group G is FTF if and only if R is left FTF, where e is a neutral element of G. This provides new examples of left FTF rings. Some consequences of this Theorem are given.

Categorical methods in graded ring theory.

Angel del Río (1992)

Publicacions Matemàtiques


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. ...

A Morita type theorem for a sort of quotient categories

Simion Breaz (2005)

Czechoslovak Mathematical Journal


We consider the quotient categories of two categories of modules relative to the Serre classes of modules which are bounded as abelian groups and we prove a Morita type theorem for some equivalences between these quotient categories.