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Proof reveals that surjunctive groups satisfy Kaplansky’s conjecture, indicating implications for group rings.
Using algebraic geometry methods, the third author proved that the group ring of a surjunctive group with coefficients in a field is always stably finite. In other words, every group satisfying Gottschalk’s conjecture also satisfies Kaplansky’s stable finiteness conjecture. Here, we present a proof of this result based on the first-order model theory.
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Ceccherini‐Silberstein et al. (2025) studied this question.
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