Non-trivial units of complex group rings
Giles Gardam
TL;DR
This paper discusses the failure of the Kaplansky unit conjecture in characteristic zero for group rings, highlighting a significant counterexample in algebra.
Contribution
It provides a counterexample demonstrating that the Kaplansky unit conjecture does not hold in characteristic zero, challenging previous assumptions.
Findings
The Kaplansky unit conjecture is false in characteristic zero.
Counterexamples exist for complex group rings.
The paper advances understanding of units in group rings.
Abstract
The Kaplansky unit conjecture for group rings is false in characteristic zero.
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Taxonomy
TopicsAdvanced Topics in Algebra · Rings, Modules, and Algebras · Algebraic structures and combinatorial models