Kummer Elements in Cyclic Algebras of Degree 5
Adam Chapman
TL;DR
This paper investigates the structure of Kummer elements in cyclic algebras of degree 5, constructing a graph to analyze their relationships and identifying conditions for chains with specific multiplicative properties.
Contribution
It introduces a graph-based framework for Kummer elements in degree 5 cyclic algebras and provides new conditions for element connectivity via Kummer chains.
Findings
Established a graph model for Kummer elements in degree 5
Derived sufficient conditions for chains connecting Kummer elements
Identified properties of multiplicative commutators in these chains
Abstract
We construct a graph of Kummer elements in a given cyclic algebra of prime degree and study its properties. In case of degree 5, we provide sufficient conditions for two elements to have a chain of Kummer elements connecting them, such that the multiplicative commutator of any two consecutive elements in the chain is a root of unity.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Rings, Modules, and Algebras · Advanced Algebra and Logic