CORDIS Project
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This project investigates group rings in mathematics, aiming to construct counterexamples to longstanding conjectures about zero divisors and direct finiteness. By leveraging modern computational techniques, it seeks to advance understanding of group properties and contribute to various mathematical theories.
Group rings are key objects in many fields of mathematics including algebra, topology, operator algebras and representation theory.
Fundamental questions about them remain unanswered, in particular several conjectures attributed to Kaplansky.
For torsion-free groups and field coefficients, the zero divisor conjecture predicts the absence of zero divisors and the idempotent conjecture predicts that 0 and 1 are the only idempotents in the group ring.
The direct finiteness conjecture says that left…
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