Crossed Product-Like and Pre-Crystalline Graded Rings
Author
Editor
- Sergei Silvestrov
- Eugen Paal
- Viktor Abramov
- Alexander Stolin
Summary, in English
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.
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.
Department/s
Publishing year
2009
Language
English
Pages
281-296
Publication/Series
Generalized Lie Theory in Mathematics, Physics and Beyond
Links
Document type
Book chapter
Publisher
Springer
Topic
- Mathematics
Status
Published
Project
- Non-commutative Analysis of Dynamics, Fractals and Wavelets
- Non-commutative Geometry in Mathematics and Physics
Research group
- Non-commutative Geometry
ISBN/ISSN/Other
- ISBN: 978-3-540-85331-2