When is R-gr equivalent to the category of modules?

AbstractIn the first part of this paper, we characterize graded rings R=⊕σ∈GRσ for which the category R-gr is equivalent with a category of modules over a certain ring.In the second part, sufficient conditions are given for the following implication to hold: if R-gr is equivalent with R1-mod (1 is the unit element of G), then R is a strongly graded ring

Coarsening of graded local cohomology

Some criteria for graded local cohomology to commute with coarsening functors are proven, and an example is given where graded local cohomology does not commute with coarsening.Comment: minor correction

The Ideal Intersection Property for Groupoid Graded Rings

We show that if a groupoid graded ring has a certain nonzero ideal property, then the commutant of the center of the principal component of the ring has the ideal intersection property, that is it intersects nontrivially every nonzero ideal of the ring. Furthermore, we show that for skew groupoid algebras with commutative principal component, the principal component is maximal commutative if and only if it has the ideal intersection property