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Noncrossed Product Matrix Subrings and Ideals of Graded Rings

In English

Författare

  • Johan Öinert
  • Patrik Lundström

Summary, in English

We show that if a groupoid graded ring has a certain nonzero ideal property and the principal component of the ring is commutative, then the intersection of a nonzero twosided ideal of the ring with the commutant of the principal component of the ring is nonzero. Furthermore, we show that for a skew groupoid ring with commutative principal component, the principal component is maximal commutative if and only if it is intersected nontrivially by each nonzero ideal of the skew groupoid ring. We also determine the center of strongly groupoid graded rings in terms of an action on the ring induced by the grading. In the end of the article, we show that, given a finite groupoid G, which has a nonidentity morphism, there is a ring, strongly graded by G, which is not a crossed product over G.

Avdelning/ar

Publiceringsår

2009

Språk

Engelska

Publikation/Tidskrift/Serie

Preprints in Mathematical Sciences

Volym

2009

Issue

10

Dokumenttyp

Artikel i tidskrift

Förlag

Lund University

Ämne

  • Mathematics

Nyckelord

  • ideals
  • matrix rings
  • Category graded rings
  • crossed products

Status

Unpublished

Projekt

  • Non-commutative Analysis of Dynamics, Fractals and Wavelets
  • Non-commutative Geometry in Mathematics and Physics

Forskningsgrupp

  • Non-commutative Geometry

ISBN/ISSN/Övrigt

  • ISSN: 1403-9338
  • LUTFMA-5112-2009