Geodesic
On coefficient fields
Glasgow mathematical journal, Tome 4 (1958) no. 1, pp. 42-48

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

Let Q be a complete local ring which has the same characteristic as its residue field P, and, for the present, let us denote by A the image of a subset A of Q under the natural homomorphism of Q onto P. Then a subfield F of Q is called a coefficient field if = P. It has been shown in [2] and in [3] that a complete equicharacteristic local ring, such as the above, always possesses at least one coefficient field; this is the embedding theorem for the equicharacteristic case. 
Geddes, A. On coefficient fields. Glasgow mathematical journal, Tome 4 (1958) no. 1, pp. 42-48. doi: 10.1017/S2040618500033840
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[1] 1.Chevalley, C., On the theory of local rings, Ann. Math., 44 (1943), 690–708. Google Scholar | DOI

[2] 2.Cohen, I. S., On the structure and ideal theory of complete local rings, Trans. Amer. Math. Soc., 59 (1946), 54–106. Google Scholar | DOI

[3] 3.Geddes, A., A short proof of the existence of coefficient fields for complete equicharacteristic local rings, J. London Math. Soc., 29 (1954), 334–341. Google Scholar | DOI

[4] 4.Geddes, A., On the embedding theorems for complete local rings, Proc London Math. Soc.(3), 6 (1956), 343–354. Google Scholar | DOI

[5] 5.Zariski, O. and Samuel, P., Commutative Algebra (Volume 1) (Princeton, 1958). Google Scholar

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