### Unit conjecture disproved!

There are three conjectures about group rings of torsion-free groups that are attributed to Kaplansky. To state them, let \(K\) be a field, \(G\) be a torsion-free group and denote by \(K[G]\) the corresponding group ring. The unit conjecture states that every unit in \(K[G]\) is of the form \(kg\) for \(k \in K\setminus\{0\}\) and … Continue reading "Unit conjecture disproved!"

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