Abstract
Let K be a field of characteristic zero, and let R be a ring containing K. Then either \(R^\times = K^\times \) or \(K^\times \) is a subgroup of infinite index in \(R^\times \).
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Benson, D.J. Rings containing a field of characteristic zero. Arch. Math. 109, 413–414 (2017). https://doi.org/10.1007/s00013-017-1100-x
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DOI: https://doi.org/10.1007/s00013-017-1100-x