let r be a ring,  be an endomorphism of r and mr be a -rigid module. amodule mr is called quasi-baer if the right annihilator of a principal submodule of r isgenerated by an idempotent. it is shown that an r-module mr is a quasi-baer module if andonly if m[[x]] is a quasi-baer module over the skew power series ring r[[x; ]].

in this paper, we investigate various kinds of extensions of twin-good rings. moreover, we prove that every element of an abelian neat ring r is twin-good if and only if r has no factor ring isomorphic to z2  or z3. the main result of [24] states some conditions that any right self-injective ring r is twin-good. we extend this result to any regular baer ring r by proving that every element of a...

Let $(R, m)$ be a commutative noetherian local ring and let $Gamma$ be a finite group. It is proved that if $R$ admits a dualizing module, then the group ring $Rga$ has a dualizing bimodule as well. Moreover, it is shown that a finitely generated $Rga$-module $M$ has generalized Gorenstein dimension zero if and only if it has generalized Gorenstein dimension zero as an $R$-module.

It is proved that every commutative ring whose RD-injective modules are Σ-RD-injective is the product of a pure semi-simple ring and a finite ring. A complete characterization of commutative rings for which each artinian (respectively simple) module is RD-injective, is given. These results can be obtained by using the properties of RD-flat modules and RD-coflat modules which are respectively th...

In [15], Kaplansky introduced Baer rings as rings in which every right (left) annihilator ideal is generated by an idempotent. According to Clark [9], a ring R is called quasi-Baer if the right annihilator of every right ideal is generated (as a right ideal) by an idempotent. Further works on quasi-Baer rings appear in [4, 6, 17]. Recently, Birkenmeier et al. [8] called a ring R to be a right (...

We consider a polynomial ring S in n variables over a finite field k of characteristic p and an action of a finite group G on S by homogeneous linear substitutions. This is equivalent to taking the symmetric powers of an n-dimensional kG-module. We want to understand S as a kG-module in a manner as explicit as possible. The ideal solution would be to give a decomposition into indecomposable sum...

We give an exposition and generalization of Orlov’s theorem on graded Gorenstein rings. We show the theorem holds for non-negatively graded rings which are Gorenstein in an appropriate sense and whose degree zero component is an arbitrary non-commutative right noetherian ring of finite global dimension. A short treatment of some foundations for local cohomology and Grothendieck duality at this ...

Talk 1 (18.10.2017 – Gesina Schwalbe): Overview of some classical results. Recall the classical theorems of Freudenthal and Hurewicz and some elementary calculations of homotopy groups of spheres. Recall the definition of the stable homotopy groups of spheres and explain the ring structure. Show that the Hopf maps are stably essential, i.e. not stably null-homotopic, using Steenrod operations. ...

For a left and right Noetherian ring $R$, we give some equivalent characterizations for $\_RR$ satisfying the Auslander condition in terms of flat (resp. injective) dimensions minimal injective coresolution resolution) $R$-modules. Furthermore, prove that an artin algebra $R$ condition, is Gorenstein if only subcategory consisting finitely generated modules contravariantly finite. As applicatio...