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Matematicheskie Zametki, 2025, Volume 117, Issue 1, Pages 121–127
DOI: https://doi.org/10.4213/mzm14263 (Mi mzm14263) 		 
Fields of algebraic numbers whose multiplicative groups are free modulo the group of units

K. N. Ponomarev

Novosibirsk State Technical University
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DOI: https://doi.org/10.4213/mzm14263
Abstract: It is shown that the multiplicative group of an algebraic number field is free modulo the group of units if the group of values of any non-Archimedean valuation of this field forms a free group.
Keywords: field, field of algebraic numbers, field valuation, non-Archimedean valuation, group of units of a field of algebraic numbers, free group.
Received: 14.02.2024
Published: 13.05.2025
English version:
Mathematical Notes, 2025, Volume 117, Issue 1, Pages 132–137
DOI: https://doi.org/10.1134/S0001434625010122
Bibliographic databases:
Document Type: Article
UDC: 512.623
MSC: 12E30
Language: Russian
Citation: K. N. Ponomarev, “Fields of algebraic numbers whose multiplicative groups are free modulo the group of units”, Mat. Zametki, 117:1 (2025), 121–127; Math. Notes, 117:1 (2025), 132–137
Citation in format AMSBIB
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\pages 121--127
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\pages 132--137
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