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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 2025 Volume 117, Issue 1, Pages 121–127 (Mi mzm14263)

Fields of algebraic numbers whose multiplicative groups are free modulo the group of units

K. N. Ponomarev

Novosibirsk State Technical University

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.

UDC: 512.623

MSC: 12E30

Received: 14.02.2024

DOI: 10.4213/mzm14263


 English version:
Mathematical Notes, 2025, 117:1, 132–137


© Steklov Math. Inst. of RAS, 2025