Formal sums and power series over a~group
Sbornik. Mathematics, Tome 191 (2000) no. 7, pp. 955-971
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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.).
@article{SM_2000_191_7_a1,
author = {N. I. Dubrovin},
title = {Formal sums and power series over a~group},
journal = {Sbornik. Mathematics},
pages = {955--971},
publisher = {mathdoc},
volume = {191},
number = {7},
year = {2000},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2000_191_7_a1/}
}
N. I. Dubrovin. Formal sums and power series over a~group. Sbornik. Mathematics, Tome 191 (2000) no. 7, pp. 955-971. http://geodesic.mathdoc.fr/item/SM_2000_191_7_a1/