caa a22 4500 60550847X CHVBK 20210128100636.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s00010-014-0282-6 doi (NATIONALLICENCE)springer-10.1007/s00010-014-0282-6 On one-dimensional formal group laws in characteristic zero [Elektronische Daten] [Harald Fripertinger, Jens Schwaiger] Let $${\mathbb{K}}$$ K be a field of characteristic zero or, more generally, a $${\mathbb{Q}}$$ Q -algebra. A formal power series $${F(x,y)=x+y+ \sum_{i,j \geq 1} a_{i,j}x^iy^j \in \mathbb{K}{[\![} x, y{]\!]}}$$ F ( x , y ) = x + y + ∑ i , j ≥ 1 a i , j x i y j ∈ K [ [ x , y ] ] is called a one-dimensional formal group law if F(F(x, y), z)=F(x, F(y, z)). Using some elementary methods, we prove that for every one-dimensional formal group law F(x, y) there exists a formal power series $${f(x)=x+\sum_{n\geq 2}f_nx ^n \in \mathbb{K}{[\![} x, y{]\!]}}$$ f ( x ) = x + ∑ n ≥ 2 f n x n ∈ K [ [ x , y ] ] so that F(x, y)=f −1(f(x)+f(y)). Springer Basel, 2014 Fripertinger Harald Institut für Mathematik und Wissenschaftliches Rechnen, NAWI-Graz, Universität Graz, Heinrichstr. 36/4, 8010, Graz, Austria aut Schwaiger Jens Institut für Mathematik und Wissenschaftliches Rechnen, NAWI-Graz, Universität Graz, Heinrichstr. 36/4, 8010, Graz, Austria aut Aequationes mathematicae Springer Basel 89/3(2015-06-01), 857-862 0001-9054 89:3<857 2015 89 10 https://doi.org/10.1007/s00010-014-0282-6 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00010-014-0282-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Fripertinger Harald Institut für Mathematik und Wissenschaftliches Rechnen, NAWI-Graz, Universität Graz, Heinrichstr. 36/4, 8010, Graz, Austria aut NATIONALLICENCE 700 1- Schwaiger Jens Institut für Mathematik und Wissenschaftliches Rechnen, NAWI-Graz, Universität Graz, Heinrichstr. 36/4, 8010, Graz, Austria aut NATIONALLICENCE 773 0- Aequationes mathematicae Springer Basel 89/3(2015-06-01), 857-862 0001-9054 89:3<857 2015 89 10