Title
Maximal graded orders over crystalline graded ringsMaximal graded orders over crystalline graded rings
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Research group
Fundamental Mathematics
Publication type
article
Publication
New York, N.Y.,
Subject
Mathematics
Source (journal)
Journal of algebra. - New York, N.Y.
Volume/pages
324(2010):6, p. 1229-1258
ISSN
0021-8693
ISI
000281525400006
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
Crystalline graded rings are generalizations of certain classes of rings like generalized twisted group rings, generalized Weyl algebras, and generalized skew crossed products. Under certain conditions, in particular, the group is finite, it is proven that the global dimension of a crystalline graded ring coincides with the global dimension of its base ring. When, in addition, the base ring is a commutative Dedekind domain, two constructions are given for producing maximal graded orders. On the way, a new concept appears, so-called, spectrally twisted group. Some general properties of it are studied. At the end of the paper several examples are considered.
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