Bimodules in Group Graded Rings

Group - Graded Rings and Duality

We give an alternative construction of the duality between finite group actions and group gradings on rings which was shown by Cohen and Montgomery in [1]. This duality is then used to extend known results on skew group rings to corresponding results for large classes of group-graded rings. Finally we modify the construction slightly to handle infinite groups. Introduction. In the first section...

Endomorphism rings of bimodules

On the Jacobson radical of strongly group graded rings

For any non-torsion group G with identity e, we construct a strongly G-graded ring R such that the Jacobson radical J(Re) is locally nilpotent, but J(R) is not locally nilpotent. This answers a question posed by Puczy lowski.

Tight Closure in Graded Rings

This paper facilitates the computation of tight closure by giving giving upper and lower bounds on the degrees of elements that need to be checked for inclusion in the tight closure of certain homogeneous ideals in a graded ring. Differential operators are introduced to the study of tight closure, and used to prove that the degree of any element in the tight closure of a homogeneous ideal (but ...

Approximate Roots in Graded Rings

An approximate root of an univariate polynomial over a graded ring A is an element in A for which the evaluated polynomial vanishes up to a prescribed order. We give an algorithm for deciding existence of approximate roots and computing essentially all of them. Based on this algorithm we also suggest a finite representation for multivariate algebraic power series.