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The domain question for the Nielsen-Soelberg group rings: the commutative case, with certified ball checks
Nielsen and Soelberg exhibited three torsion-free groups G_1, G_2, G_3 carrying 8-element sets without unique products, and asked whether any of the group rings R[G_i], R a domain, is a domain. We record that for every commutative domain R the answer is affirmative for all three groups: each G_i is
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