Is there an infinite field whose multiplicative group is indecomposable?

Sunil K. Chebolu () and Keir Lockridge ()
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Sunil K. Chebolu: Illinois State University
Keir Lockridge: Gettysburg College

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 2, 398-403

Abstract: 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.

Keywords: Fermat primes; Mersenne primes; Indecomposable abelian groups; Perfect fields; Valued fields; Primary 12E20; Secondary 11D41; 20K20 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13226-022-00261-6

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