Geodesic
Inertial Isomorphisms of V-Rings
Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 529-539

Voir la notice de l'article provenant de la source Cambridge University Press

Throughout this paper R and Rn will denote v-rings, that is, complete discrete rank-one valuation rings of characteristic zero, having a common residue field k of characteristic p. R is assumed unramified and Rn has ramification index n. Let π be a prime element in Rn. Then Rn = R[π], where π is a root of an Eisenstein polynomial ƒ = xn + pƒn-1 xn-1 + ... + pƒ0 with coefficients in R and ƒ 0 a unit. Thus Rn is inertially isomorphic to R[[x]]/ƒR[(x)], that is, the rings are isomorphic by a mapping which induces the identity mapping on the common residue field. R[[x]] represents the power series ring in the indeterminate x over R. In this paper we identify Rn with R[[x]]/ƒR[[x]], R with its natural embedding in Rn and π with x + ƒR[[x]]. 
Heerema, N. Inertial Isomorphisms of V-Rings. Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 529-539. doi: 10.4153/CJM-1967-046-2
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