Overview
The mathematician Irving Kaplansky is notable for proposing numerous conjectures in several branches of mathematics, including a list of ten conjectures on Hopf algebras. They are usually known as Kaplansky's conjectures.
Group rings
Let be a field, and a torsion-free group. Kaplansky's zero divisor conjecture states:
The group ring does not contain nontrivial zero divisors, that is, it is a domain.
Two related conjectures are known as, respectively, Kaplansky's idempotent conjecture:
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