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 Mat. Sb., 2000, Volume 191, Number 7, Pages 13–30 (Mi msb490)

Formal sums and power series over a group

N. I. Dubrovin

Abstract: Formal series over a group are studied as an algebraic system with componentwise composition and a partial operation of convolution “$*$”. For right-ordered groups a module of formal power series is introduced and studied; these are formal sums with well-ordered supports. Special attention is paid to systems of formal power series (whose supports are well-ordered with respect to the ascending order) that form an $L$-basis, that is, such that every formal power series can be expanded uniquely in this system. $L$-bases are related to automorphisms of the module of formal series that have natural properties of monotonicity and $\sigma$-linearity. The relations $\gamma*\beta=0$ and $\gamma*\beta=1$ are also studied. Note that in the case of a totally ordered group the system of formal power series forms a skew field with valuation (Mal'tsev–Neumann, 1948–1949.).

DOI: https://doi.org/10.4213/sm490

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English version:
Sbornik: Mathematics, 2000, 191:7, 955–971

Bibliographic databases:

UDC: 512.8
MSC: Primary 16S99, 16S34; Secondary 06F15, 20F60, 20C-07, 20F99

Citation: N. I. Dubrovin, “Formal sums and power series over a group”, Mat. Sb., 191:7 (2000), 13–30; Sb. Math., 191:7 (2000), 955–971

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/msb490
• https://doi.org/10.4213/sm490
• http://mi.mathnet.ru/eng/msb/v191/i7/p13

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. N. I. Dubrovin, “Rational operators of the space of formal series”, J. Math. Sci., 149:3 (2008), 1191–1223
2. A. M. Meirmanov, “Derivation of equations of seismic and acoustic wave propagation and equations of filtration via homogenization of periodic structures”, Journal of Mathematical Sciences (New York), 2009
3. Graeter J. Sperner R.P., “On Embedding Left-Ordered Groups Into Division Rings”, Forum Math., 27:1 (2015), 485–518
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