Abstract
In [2], we determined the finite fields with indecomposable multiplicative groups and conjectured that there is no infinite field whose multiplicative group is indecomposable. In this paper, we prove this conjecture for several popular classes of fields, including finitely generated fields, discrete valued fields, fields of Hahn series, local fields, global fields, and function fields.
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Communicated by B.Sury.
The first author is supported by Simons Foundation: Collaboration Grant for Mathematicians (516354).
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Chebolu, S.K., Lockridge, K. Is there an infinite field whose multiplicative group is indecomposable?. Indian J Pure Appl Math 54, 398–403 (2023). https://doi.org/10.1007/s13226-022-00261-6
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DOI: https://doi.org/10.1007/s13226-022-00261-6