Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Separable Groupoid Rings
University West, Department of Technology, Mathematics and Computer Science, Division for Mathematics and Sciences.ORCID iD: 0000-0001-6594-7041
2006 (English)In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 34, no 8, p. 3029-3041Article 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, p. 3029-3041
Keywords [en]
Graded module; Graded ring; Separable functor; Separable ring extension
Keywords [sv]
abstrakt algebraisk geometri
National Category
Algebra and Logic
Research subject
ENGINEERING, Mathematics
Identifiers
URN: urn:nbn:se:hv:diva-1825DOI: 10.1080/00927870600639906OAI: oai:DiVA.org:hv-1825DiVA, id: diva2:272698
Available from: 2009-10-16 Created: 2009-10-16 Last updated: 2019-11-18Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full text

Search in DiVA

By author/editor
Lundström, Patrik
By organisation
Division for Mathematics and Sciences
In the same journal
Communications in Algebra
Algebra and Logic

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 375 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf