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Commutativity and ideals in strongly graded rings
Lund University.
Lund University. (Mathematics/Applied Mathematics)ORCID iD: 0000-0003-4554-6528
Aristotle University of Thessaloniki, Greece .
Aristotle University of Thessaloniki, Greece .
2009 (English)In: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications, ISSN 0167-8019, E-ISSN 1572-9036, Vol. 108, no 3, 585-602 p.Article in journal (Refereed) Published
Abstract [en]

In some recent papers by the first two authors it was shown that for any algebraic crossed product A, where A0, the subring in the degree zero component of the grading, is a commutative ring, each non-zero two-sided ideal in A has a non-zero intersection with the commutant CA(A0) of A0 in 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 A0, 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 A0, and this is done both for strongly graded rings and crystalline graded rings.

Place, publisher, year, edition, pages
Springer, 2009. Vol. 108, no 3, 585-602 p.
Keyword [en]
Strongly graded rings, Commutativity, Ideals
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-22074DOI: 10.1007/s10440-009-9435-3ISI: 000271941500009Scopus ID: 2-s2.0-71449097997OAI: oai:DiVA.org:mdh-22074DiVA: diva2:682642
Funder
Swedish Research Council
Available from: 2013-12-28 Created: 2013-10-23 Last updated: 2014-01-10Bibliographically approved

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Publisher's full textScopushttp://dx.doi.org/10.1007/s10440-009-9435-3

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Silvestrov, Sergei
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CiteExportLink to record
Permanent link

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Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
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Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
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  • Other locale
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Output format
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