Abstract
The unit conjecture, commonly attributed to Kaplansky, predicts that if $K$ is a field and $G$ is a torsion-free group, then the only units of the group ring $K[G]$ are the trivial units, that is, the non-zero scalar multiples of group elements. We give a concrete counterexample to this conjecture; the group is virtually abelian and the field is order two.
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mrreviewer = {Paul D. Mitchener},
doi = {10.1007/978-3-0348-8187-6},
url = {https://doi.org/10.1007/978-3-0348-8187-6},
zblnumber = {1136.58013},
}