Geodesic
Formal sums and power series over a group
Sbornik. Mathematics, Tome 191 (2000) no. 7, pp. 955-971 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.).

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