Object-unital groupoid graded rings, crossed products and separability

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 th...

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Veröffentlicht in:Communications in algebra 2021-04, Vol.49 (4), p.1676-1696
Hauptverfasser: Cala, Juan, Lundström, Patrik, Pinedo, Hector
Format: Artikel
Sprache:eng
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Zusammenfassung: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 for when object unital groupoid graded rings are separable over their principal component, thereby generalizing previous results from the unital case to a non-unital situation.
ISSN:0092-7872
1532-4125
1532-4125
DOI:10.1080/00927872.2020.1846742