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- Title
Ozone Groups and Centers of Skew Polynomial Rings.
- Authors
Chan, Kenneth; Gaddis, Jason; Won, Robert; Zhang, James J
- Abstract
We introduce the ozone group of a noncommutative algebra |$A$| , defined as the group of automorphisms of |$A$| , which fix every element of its center. In order to initiate the study of ozone groups, we study polynomial identity (PI) skew polynomial rings, which have long proved to be a fertile testing ground in noncommutative algebra. Using the ozone group and other invariants defined herein, we give explicit conditions for the center of a PI skew polynomial ring to be Gorenstein (resp. regular) in low dimension.
- Subjects
POLYNOMIAL rings; NONCOMMUTATIVE algebras; OZONE; GROUP algebras; GORENSTEIN rings; POLYNOMIALS
- Publication
IMRN: International Mathematics Research Notices, 2024, Vol 2024, Issue 7, p5689
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnad235