Kaplansky conjecture

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In mathematics, the Kaplansky conjecture on group rings states that the complex group ring CG of a torsion-free group G has no nontrivial zero divisors, i.e. that for x,y in CG with xy = 0, either x = 0 or y = 0.

There are numerous other 'Kaplansky conjectures': a list of ten on Hopf algebras, on quadratic forms, in group theory, the Kadison-Kaplansky conjecture.

[edit] References

  • Lück, W. 2002. L2-Invariants: Theory and Applications to Geometry and K-Theory. Berlin:Springer. ISBN 3-540-43566-2.
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