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Separable Groupoid Rings
University West, Department of Technology, Mathematics and Computer Science, Division for Mathematics and Sciences.
2006 (English)In: Communications in Algebra, ISSN 0092-7872, Vol. 34, no 8, 3029-3041 p.Article in journal (Refereed) Published
Abstract [en]

We show that groupoid rings are separable over their ring of coefficients if and only if the groupoid is finite and the orders of the associated principal groups are invertible in the ring of coefficients. We use this to show that if we are given a finite groupoid, then the associated groupoid ring is semisimple (or hereditary) if and only if the ring of coefficients is semisimple (or hereditary) and the orders of the principal groups are invertible in the ring of coefficients. To this end, we extend parts of the theory of graded rings and modules from the group graded case to the category graded, and, hence, groupoid graded situation. In particular, we show that strongly groupoid graded rings are separable over their principal components if and only if the image of the trace map contains the identity

Place, publisher, year, edition, pages
Taylor & Francis , 2006. Vol. 34, no 8, 3029-3041 p.
Keyword [en]
Graded module; Graded ring; Separable functor; Separable ring extension
Keyword [sv]
abstrakt algebraisk geometri
National Category
Mathematics
Research subject
Engineering, Mathematics
Identifiers
URN: urn:nbn:se:hv:diva-1825DOI: 10.1080/00927870600639906OAI: oai:DiVA.org:hv-1825DiVA: diva2:272698
Available from: 2009-10-16 Created: 2009-10-16 Last updated: 2009-11-03Bibliographically approved

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