Geodesic
Formal sums and power series over a group
Sbornik. Mathematics, Tome 191 (2000) no. 7, pp. 955-971
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     year = {2000},
     volume = {191},
     number = {7},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2000_191_7_a1/}
}
TY  - JOUR
AU  - N. I. Dubrovin
TI  - Formal sums and power series over a group
JO  - Sbornik. Mathematics
PY  - 2000
SP  - 955
EP  - 971
VL  - 191
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/SM_2000_191_7_a1/
LA  - en
ID  - SM_2000_191_7_a1
ER  - 
%0 Journal Article
%A N. I. Dubrovin
%T Formal sums and power series over a group
%J Sbornik. Mathematics
%D 2000
%P 955-971
%V 191
%N 7
%U http://geodesic.mathdoc.fr/item/SM_2000_191_7_a1/
%G en
%F 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/

[1] Maltsev A. I., “O vklyuchenii gruppovykh algebr v algebry s deleniem”, Dokl. AN SSSR, 60:9 (1948), 1499–1501 | MR | Zbl

[2] Dubrovina T. V., Dubrovin N. I., “Konusy v gruppakh”, Matem. sb., 187:7 (1996), 59–74 | MR | Zbl

[3] Kokorin A. I., Kopytov V. M., Lineino uporyadochennye gruppy, Nauka, M., 1972 | MR | Zbl

[4] Dubrovin N. I., “Obratimost gruppovogo koltsa pravouporyadochennoi gruppy nad telom”, Matem. zametki, 42:4 (1987), 508–518 | MR

[5] Dubrovin N. I., “Ratsionalnye zamykaniya gruppovykh kolets levouporyadochennykh grupp”, Matem. sb., 184:7 (1993), 3–48 | Zbl

[6] Dubrovin N. I., “Primer tsepnogo pervichnogo koltsa s nilpotentnymi elementami”, Matem. sb., 120 (162):3 (1983), 441–447 | MR | Zbl