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Separable Groupoid Rings
Högskolan Väst, Institutionen för teknik, matematik och datavetenskap, Avd för matematik och naturvetenskap.
2006 (engelsk)Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 34, nr 8, s. 3029-3041Artikkel i tidsskrift (Fagfellevurdert) 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

sted, utgiver, år, opplag, sider
Taylor & Francis , 2006. Vol. 34, nr 8, s. 3029-3041
Emneord [en]
Graded module; Graded ring; Separable functor; Separable ring extension
Emneord [sv]
abstrakt algebraisk geometri
HSV kategori
Forskningsprogram
Teknik, Matematik
Identifikatorer
URN: urn:nbn:se:hv:diva-1825DOI: 10.1080/00927870600639906OAI: oai:DiVA.org:hv-1825DiVA, id: diva2:272698
Tilgjengelig fra: 2009-10-16 Laget: 2009-10-16 Sist oppdatert: 2017-12-12bibliografisk kontrollert

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Totalt: 211 treff
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