Locally PI but not PI Division Rings of Arbitrary GK-Dimension
J. C. McConnell, A. R. Wadsworth
TL;DR
This paper constructs examples of division rings with arbitrary Gelfand-Kirillov dimension that are locally polynomial identity but not globally PI, expanding understanding of their structural diversity.
Contribution
It provides the first known examples of locally PI but not PI division rings for any positive GK-dimension, demonstrating their existence across all dimensions.
Findings
Examples of locally PI but not PI division rings for all positive GK-dimensions.
These rings exhibit diverse algebraic properties not previously documented.
The results deepen the understanding of the relationship between local and global polynomial identities.
Abstract
We give examples of locally PI but not PI division rings of GK-dimension n for every positive integer n.
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Taxonomy
TopicsRings, Modules, and Algebras · Algebraic structures and combinatorial models · Advanced Topics in Algebra