On radicals of infinite matrix rings

Differential Polynomial Rings of Triangular Matrix Rings

A Note on Radicals of Seminear-rings

We generalize a few results of [2, 6, 8] for radical classes of rings for radical classes of seminear-rings by using the construction for radical classes of seminear-rings. AMS Mathematics Subject Classification (2000): 16Y60, 16W50

On Cohomology rings of infinite groups

Let R be any ring (with 1), G a torsion free group and RG the corresponding group ring. Let Ext∗RG(M,M) be the cohomology ring associated to the RG-module M . Let H be a subgroup of finite index of G. The following is a special version of our main Theorem: Assume the profinite completion of G is torsion free. Then an element ζ ∈ Ext∗RG(M,M) is nilpotent (under Yoneda’s product) if and only if i...

Stably Just Infinite Rings

We study just infinite algebras which remain so upon extension of scalars by arbitrary field extensions. Such rings are called stably just infinite. We show that just infinite rings over algebraically closed fields are stably just infinite provided that the ring is either right noetherian (4.2) or countably generated over a large field (6.4). We give examples to show that, over countable fields...

On the Complexity of Radicals in Noncommutative Rings

This article expands upon the recent work by Downey, Lempp, and Mileti [3], who classified the complexity of the nilradical and Jacobson radical of commutative rings in terms of the arithmetical hierarchy. Let R be a computable (not necessarily commutative) ring with identity. Then it follows from the definitions that the prime radical of R is Π1, and the Levitzki radical of R is Π 0 2. We show...