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Commutativity and Ideals in Strongly Graded Rings

Öinert, Johan LU ; Silvestrov, Sergei LU ; Theohari-Apostolidi, Theodora and Vavatsoulas, Harilaos (2009) In Acta Applicandae Mathematicae 108(3). p.585-602
Abstract
In some recent papers by the first two authors it was shown that for any algebraic crossed product A, where A(0), 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 C-A(A(0)) of A(0) 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 A(0), the degree zero component of the grading, is a commutative ring. We also give a description of the intersection... (More)
In some recent papers by the first two authors it was shown that for any algebraic crossed product A, where A(0), 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 C-A(A(0)) of A(0) 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 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 A(0), and this is done both for strongly graded rings and crystalline graded rings. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Strongly graded rings, Commutativity, Ideals
in
Acta Applicandae Mathematicae
volume
108
issue
3
pages
585 - 602
publisher
Springer
external identifiers
  • wos:000271941500009
  • scopus:71449097997
ISSN
0167-8019
DOI
10.1007/s10440-009-9435-3
language
English
LU publication?
yes
id
00b17989-6444-444e-92f2-b4e80f2508a9 (old id 1518589)
date added to LUP
2009-12-28 15:18:20
date last changed
2017-01-01 05:32:30
@article{00b17989-6444-444e-92f2-b4e80f2508a9,
  abstract     = {In some recent papers by the first two authors it was shown that for any algebraic crossed product A, where A(0), 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 C-A(A(0)) of A(0) 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 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 A(0), and this is done both for strongly graded rings and crystalline graded rings.},
  author       = {Öinert, Johan and Silvestrov, Sergei and Theohari-Apostolidi, Theodora and Vavatsoulas, Harilaos},
  issn         = {0167-8019},
  keyword      = {Strongly graded rings,Commutativity,Ideals},
  language     = {eng},
  number       = {3},
  pages        = {585--602},
  publisher    = {Springer},
  series       = {Acta Applicandae Mathematicae},
  title        = {Commutativity and Ideals in Strongly Graded Rings},
  url          = {http://dx.doi.org/10.1007/s10440-009-9435-3},
  volume       = {108},
  year         = {2009},
}