Acta Applicandae Mathematicae

, Volume 108, Issue 3, pp 585–602 | Cite as

Commutativity and Ideals in Strongly Graded Rings

  • Johan Öinert
  • Sergei Silvestrov
  • Theodora Theohari-Apostolidi
  • Harilaos Vavatsoulas


In some recent papers by the first two authors it was shown that for any algebraic crossed product \(\mathcal {A}\) , where \(\mathcal {A}_{0}\) , the subring in the degree zero component of the grading, is a commutative ring, each non-zero two-sided ideal in \(\mathcal {A}\) has a non-zero intersection with the commutant \(C_{\mathcal {A}}(\mathcal {A}_{0})\) of \(\mathcal {A}_{0}\) in \(\mathcal {A}\) . This result has also been generalized to crystalline graded rings; a more general class of graded rings to which algebraic crossed products belong. In this paper we generalize this result in another direction, namely to strongly graded rings (in some literature referred to as generalized crossed products) where the subring \(\mathcal {A}_{0}\) , the degree zero component of the grading, is a commutative ring. We also give a description of the intersection between arbitrary ideals and commutants to bigger subrings than \(\mathcal {A}_{0}\) , and this is done both for strongly graded rings and crystalline graded rings.


Strongly graded rings Commutativity Ideals 

Mathematics Subject Classification (2000)

16W50 13A02 16D25 46H10 


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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Johan Öinert
    • 1
  • Sergei Silvestrov
    • 1
  • Theodora Theohari-Apostolidi
    • 2
  • Harilaos Vavatsoulas
    • 2
  1. 1.Centre for Mathematical SciencesLund UniversityLundSweden
  2. 2.Department of MathematicsAristotle University of ThessalonikiThessalonikiGreece

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