Geodesic
Fields with two linear orderings
Matematičeskie zametki, Tome 7 (1970) no. 5, pp. 525-536 Cet article a éte moissonné depuis la source Math-Net.Ru

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We characterize fields which are maximal with respect to the property of having two different linear orderings. The Galois group of the algebraic closure of a maximal field is described. An example of non-uniqueness of the maximal extension is mentioned. 
@article{MZM_1970_7_5_a0,
     author = {S. V. Bredikhin and Yu. L. Ershov and V. G. Kal'nei},
     title = {Fields with two linear orderings},
     journal = {Matemati\v{c}eskie zametki},
     pages = {525--536},
     year = {1970},
     volume = {7},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_7_5_a0/}
}
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S. V. Bredikhin; Yu. L. Ershov; V. G. Kal'nei. Fields with two linear orderings. Matematičeskie zametki, Tome 7 (1970) no. 5, pp. 525-536. http://geodesic.mathdoc.fr/item/MZM_1970_7_5_a0/