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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb., 2020 Volume 211, Number 9, Pages 3–23 (Mi sm9286)

Stable decomposability of matrices over the rational closure of a group algebra of an ordered group

N. I. Dubrovin

Vladimir State University, Vladimir, Russia

Abstract: Under the assumption that the rational closure of a group algebra of a left-ordered group in the ring of operators of the module of formal Malcev series is a division ring, we find a canonical form of nonsingular matrices of this division ring.
Bibliography: 10 titles.

Keywords: right-ordered groups, division ring of fractions, formal series.

UDC: 512.552+512.555

MSC: Primary 20C07; Secondary 06F15, 16K40, 16W60

Received: 02.06.2019 and 16.05.2020

DOI: 10.4213/sm9286


 English version:
Sbornik: Mathematics, 2020, 211:9, 1213–1232

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© Steklov Math. Inst. of RAS, 2025