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
1 Citations
GRADED MODULES OVER OBJECT-UNITAL GROUPOID GRADED RINGS
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-modExpand

References

SHOWING 1-10 OF 51 REFERENCES
{m
TLDR
The master programme in Applied Geology aims to provide comprehensive knowledge based on various branches of Geology, with special focus on Applied geology subjects in the areas of Geomorphology, Structural geology, Hydrogeology, Petroleum Geologists, Mining Geology), Remote Sensing and Environmental geology. Expand
EPSILON-STRONGLY GROUPOID-GRADED RINGS, THE PICARD INVERSE CATEGORY AND COHOMOLOGY
Abstract We introduce the class of partially invertible modules and show that it is an inverse category which we call the Picard inverse category. We use this category to generalize the classicalExpand
A survey of s-unital and locally unital rings
We gather some classical results and examples that show strict inclusion between the families of unital rings, rings with enough idempotents, rings with sets of local units, locally unital rings,Expand
Separability in algebra and category theory
Separable field extensions are essentially known since the 19th century and their formal definition was given by Ernst Steinitz in 1910. In this survey we first recall this notion and equivalentExpand
On the separability of the partial skew groupoid ring
Given a partial (resp. a global) action $$\alpha $$α of a connected finite groupoid $$\mathscr {G}$$G on a ring $$\mathcal {A},$$A, we determine necessary and sufficient conditions for the partialExpand
  • 2016
  • Bull. Math. Soc. Sci. Math. Roumanie
  • 2013
Firm Frobenius monads and firm Frobenius algebras
Firm Frobenius algebras are firm algebras and counital coalgebras such that the comultiplication is a bimodule map. They are investigated by categorical methods based on a study of adjunctions andExpand
Firm monads and firm Frobenius algebras
  • Bull. Math. Soc. Sci. Math. Roumanie
  • 2013
  • Int. Electron. J. Algebra
  • 2012
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