Geodesic
The Makar-Limanov algebraically closed skew field
Algebra i logika, Tome 39 (2000) no. 6, pp. 662-692.

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We re-prove the Makar-Limanov theorem on the existence of an algebraically closed skew field in the sense of there being a solution for any (generalized) polynomial equation. A new example of such a skew field is presented in which the Makar-Limanov construction is contained as a skew subfield. Our reasoning is underpinned by the main ideas of the original proof, but we employ a simpler argument for proving that the skew field constructed is algebraically closed. 
@article{AL_2000_39_6_a2,
     author = {P. S. Kolesnikov},
     title = {The {Makar-Limanov} algebraically closed skew field},
     journal = {Algebra i logika},
     pages = {662--692},
     publisher = {mathdoc},
     volume = {39},
     number = {6},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2000_39_6_a2/}
}
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P. S. Kolesnikov. The Makar-Limanov algebraically closed skew field. Algebra i logika, Tome 39 (2000) no. 6, pp. 662-692. http://geodesic.mathdoc.fr/item/AL_2000_39_6_a2/