Endre søk
RefereraExporteraLink to record
Permanent link

Direct link
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Annet format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annet språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf
Bimodules in Group Graded Rings
Blekinge Tekniska Högskola, Fakulteten för teknikvetenskaper, Institutionen för matematik och naturvetenskap.ORCID-id: 0000-0001-8095-0820
2017 (engelsk)Inngår i: Algebras and Representation Theory, ISSN 1386-923X, E-ISSN 1572-9079, Vol. 20, nr 6, s. 1483-1494Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

In this article we introduce the notion of a controlled group graded ring. Let G be a group, with identity element e, and let R = aS center dot (gaG) R (g) be a unital G-graded ring. We say that R is G-controlled if there is a one-to-one correspondence between subsets of the group G and (mutually non-isomorphic) R (e) -sub-bimodules of R, given by G aSc Ha dagger broken vertical bar aS center dot (haH) R (h) . For strongly G-graded rings, the property of being G-controlled is stronger than that of being simple. We provide necessary and sufficient conditions for a general G-graded ring to be G-controlled. We also give a characterization of strongly G-graded rings which are G-controlled. As an application of our main results we give a description of all intermediate subrings T with R (e) aS dagger T aS dagger R of a G-controlled strongly G-graded ring R. Our results generalize results for artinian skew group rings which were shown by Azumaya 70 years ago. In the special case of skew group rings we obtain an algebraic analogue of a recent result by Cameron and Smith on bimodules in crossed products of von Neumann algebras.

sted, utgiver, år, opplag, sider
SPRINGER , 2017. Vol. 20, nr 6, s. 1483-1494
Emneord [en]
Graded ring, Strongly graded ring, Crossed product, Skew group ring, Bimodule, Picard group
HSV kategori
Identifikatorer
URN: urn:nbn:se:bth-15657DOI: 10.1007/s10468-017-9696-xISI: 000416229800008OAI: oai:DiVA.org:bth-15657DiVA, id: diva2:1166130
Merknad

open access

Tilgjengelig fra: 2017-12-14 Laget: 2017-12-14 Sist oppdatert: 2025-09-30bibliografisk kontrollert

Open Access i DiVA

fulltext(451 kB)442 nedlastinger
Filinformasjon
Fil FULLTEXT01.pdfFilstørrelse 451 kBChecksum SHA-512
389182c225198c3256b51ab5953c234524c04a8f6a61be79c2aced96f2cfd979f662696be2c5820e028f3b33e3424c9562a4c4094d58720c3339cebb7157d8ff
Type fulltextMimetype application/pdf

Andre lenker

Forlagets fulltekstBimodules in Group Graded Rings

Person

Öinert, Johan

Søk i DiVA

Av forfatter/redaktør
Öinert, Johan
Av organisasjonen
I samme tidsskrift
Algebras and Representation Theory

Søk utenfor DiVA

GoogleGoogle Scholar
Totalt: 443 nedlastinger
Antall nedlastinger er summen av alle nedlastinger av alle fulltekster. Det kan for eksempel være tidligere versjoner som er ikke lenger tilgjengelige

doi
urn-nbn

Altmetric

doi
urn-nbn
Totalt: 585 treff
RefereraExporteraLink to record
Permanent link

Direct link
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Annet format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annet språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf