Commutativity and Ideals in Strongly Graded Rings
(2009) In Acta Applicandae Mathematicae 108(3). p.585602 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 nonzero twosided ideal in A has a nonzero intersection with the commutant CA(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 nonzero twosided ideal in A has a nonzero intersection with the commutant CA(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)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/1518589
 author
 Öinert, Johan ^{LU} ; Silvestrov, Sergei ^{LU} ; TheohariApostolidi, Theodora and Vavatsoulas, Harilaos
 organization
 publishing date
 2009
 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
 01678019
 DOI
 10.1007/s1044000994353
 language
 English
 LU publication?
 yes
 id
 00b179896444444e92f2b4e80f2508a9 (old id 1518589)
 date added to LUP
 20091228 15:18:20
 date last changed
 20170101 05:32:30
@article{00b179896444444e92f2b4e80f2508a9, 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 nonzero twosided ideal in A has a nonzero intersection with the commutant CA(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 TheohariApostolidi, Theodora and Vavatsoulas, Harilaos}, issn = {01678019}, keyword = {Strongly graded rings,Commutativity,Ideals}, language = {eng}, number = {3}, pages = {585602}, publisher = {Springer}, series = {Acta Applicandae Mathematicae}, title = {Commutativity and Ideals in Strongly Graded Rings}, url = {http://dx.doi.org/10.1007/s1044000994353}, volume = {108}, year = {2009}, }