Geodesic
Root Selections and 2p-th Root Selections in Hyperfields
Discussiones Mathematicae. General Algebra and Applications, Tome 39 (2019) no. 1, pp. 43-53.

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In this paper we define root selections and 2p-th root selections for hyperfields: these are multiplicative subgroups whose existence is equivalent to the existence of a well behaved square root function and 2p-th root function, respectively. We proceed to investigate some basic properties of such root selections, and draw some parallels between the theory of root selections for hyperfields and the theory of orderings and orderings of higher level in hyperfields previously studied by the author.
Keywords: square roots, orderings, orderings of higher level, hyperfields, 2p-th roots 
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Gładki, Paweł. Root Selections and 2p-th Root Selections in Hyperfields. Discussiones Mathematicae. General Algebra and Applications, Tome 39 (2019) no. 1, pp. 43-53. http://geodesic.mathdoc.fr/item/DMGAA_2019_39_1_a3/

[1] E. Artin and O. Schreier, Algebraische Konstruktion reeller Körper, Abh. Math. Sem. Univ. Hamburg 5 (1927) 85–99. doi:10.1007/BF02952512

[2] E. Artin and O. Schreier, Eine Kennzeichnung der reell abgeschlossenen Körper, Abh. Math. Sem. Univ. Hamburg 5 (1927) 225–231. doi:10.1007/BF02952522

[3] E. Becker, Hereditarily Pythagorean fields and orderings of higher level, volume 29 of Monografias de Matemática (IMPA, Rio de Janeiro, 1978).

[4] P. Gładki, N-th root selections in fields, to appear.

[5] P. Gładki, Orderings of higher level in multifields and multirings, Ann. Math. Sil. 24 (2010) 15–25.

[6] P. Gładki and M. Marshall, Orderings and signatures of higher level on multirings and hyperfields, J. K-Theory 10 (2012) 489–518. doi:10.1017/is012004021jkt189

[7] P. Gładki and M. Marshall, Witt equivalence of function fields over global fields, Trans. Amer. Math. Soc. 369 (2017) 7861–7881. doi:10.1090/tran/6898

[8] J. Jun, Algebraic geometry over hyperfields, Adv. Math. 323 (2018) 142–192. doi:10.1016/j.aim.2017.10.043

[9] M. Krasner, Approximation des corps valués complets de caractéristique p ≠ 0 par ceux de caractéristique 0, in: Colloque d’algebre supérieure, tenu a Bruxelles du 19 au 22 décembre 1956, Centre Belge de Recherches Mathématiques, pages 129–206. Établissements Ceuterick, Louvain (Librairie Gauthier-Villars, Paris, 1957).

[10] T.-Y. Lam, The theory of ordered fields, in: B.R. McDonald, editor, Ring Theory and Algebra III, volume 55 of Lecture Notes in Pure and Appl. Math., pages 1–152, (Dekker, New York, 1980).

[11] M. Marshall, Real reduced multirings and multifields, J. Pure Appl. Algebra 205 (2006) 452–468. doi:10.1016/j.jpaa.2005.07.011

[12] W. Waterhouse, Square root as homomorphism, American Math. Monthly 119 (2012) 235–239. doi:10.4169/amer.math.monthly.119.03.235