# Object-unital groupoid graded rings, crossed products and separability

@article{Cala2020ObjectunitalGG, title={Object-unital groupoid graded rings, crossed products and separability}, author={J. Cala and Patrik Lundstr{\"o}m and H. Pinedo}, journal={Communications in Algebra}, year={2020}, volume={49}, pages={1676 - 1696} }

Abstract We extend the classical construction by Noether of crossed product algebras, defined by finite Galois field extensions, to cover the case of separable (but not necessarily finite or normal) field extensions. This leads us naturally to consider non-unital groupoid graded rings of a particular type that we call object unital. We determine when such rings are strongly graded, crossed products, skew groupoid rings and twisted groupoid rings. We also obtain necessary and sufficient criteria… Expand

#### One Citation

GRADED MODULES OVER OBJECT-UNITAL GROUPOID GRADED RINGS

- 2021

In a previous article (see [6]), we introduced and analyzed ring-theoretic properties of object unital G-graded rings R, where G is a groupoid. In the present article, we analyze the category G-R-mod… Expand

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