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Object-unital groupoid graded rings, crossed products and separability
Universidad Industrial de Santander, Escuela de Matemáticas, Bucaramanga, Colombia (COL).
University West, Department of Engineering Science, Division of Mathematics, Computer and Surveying Engineering.ORCID iD: 0000-0001-6594-7041
Universidad Industrial de Santander, Escuela de Matemáticas, Bucaramanga, Colombia (COL).
2021 (English)In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 44, no 4, p. 1676-1696Article in journal (Refereed) Published
Abstract [en]

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. © 2020 The Author(s). Published with license by Taylor and Francis Group, LLC.

Place, publisher, year, edition, pages
2021. Vol. 44, no 4, p. 1676-1696
Keywords [en]
Crossed product, graded ring, groupoids, separable extension
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:hv:diva-16100DOI: 10.1080/00927872.2020.1846742ISI: 000592621100001Scopus ID: 2-s2.0-85096769377OAI: oai:DiVA.org:hv-16100DiVA, id: diva2:1507937
Note

Published online: 26 Nov 2020

Available from: 2020-12-09 Created: 2020-12-09 Last updated: 2022-01-19Bibliographically approved

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Lundström, Patrik

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