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Crossed Product-Like and Pre-Crystalline Graded Rings

Öinert, Johan LU and Silvestrov, Sergei LU (2009) In Generalized Lie Theory in Mathematics, Physics and Beyond p.281-296
Abstract
We introduce crossed product-like rings, as a natural generalization of

crystalline graded rings, and describe their basic properties. Furthermore, we prove that for certain pre-crystalline graded rings and every crystalline graded ring A, for which the base subring A_0 is commutative, each non-zero two-sided ideal has a nonzero intersection with C_A(A_0), i.e. the commutant of A_0 in A. We also show that in general this property need not hold for crossed product-like rings.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
in
Generalized Lie Theory in Mathematics, Physics and Beyond
editor
Silvestrov, Sergei; Paal, Eugen; Abramov, Viktor and Stolin, Alexander
pages
281 - 296
publisher
Springer
external identifiers
  • WOS:000264638600024
  • Scopus:79951909121
ISBN
978-3-540-85331-2
DOI
10.1007/978-3-540-85332-9_24
project
Non-commutative Analysis of Dynamics, Fractals and Wavelets
Non-commutative Geometry in Mathematics and Physics
language
English
LU publication?
yes
id
b2c514f1-a251-4499-a86f-15e86a407d1f (old id 1299465)
alternative location
http://www.springerlink.com/
date added to LUP
2009-04-14 15:50:40
date last changed
2016-10-13 04:44:24
@misc{b2c514f1-a251-4499-a86f-15e86a407d1f,
  abstract     = {We introduce crossed product-like rings, as a natural generalization of<br/><br>
crystalline graded rings, and describe their basic properties. Furthermore, we prove that for certain pre-crystalline graded rings and every crystalline graded ring A, for which the base subring A_0 is commutative, each non-zero two-sided ideal has a nonzero intersection with C_A(A_0), i.e. the commutant of A_0 in A. We also show that in general this property need not hold for crossed product-like rings.},
  author       = {Öinert, Johan and Silvestrov, Sergei},
  editor       = {Silvestrov, Sergei and Paal, Eugen and Abramov, Viktor and Stolin, Alexander},
  isbn         = {978-3-540-85331-2},
  language     = {eng},
  pages        = {281--296},
  publisher    = {ARRAY(0x9398900)},
  series       = {Generalized Lie Theory in Mathematics, Physics and Beyond},
  title        = {Crossed Product-Like and Pre-Crystalline Graded Rings},
  url          = {http://dx.doi.org/10.1007/978-3-540-85332-9_24},
  year         = {2009},
}