N-th root Selections in Fields

• Autorzy: Paweł Gładki
• Języki publikacji: EN

Abstrakty

EN

In this work we generalize the results of [9] to the higher level case: we define n-th root selections in fields of characteristic $\neq 2$, that is subgroups of the multiplicative group of a field whose existence is equivalent to the existence of a partial inverse of the $x\mapsto x^n$ function, provide necessary and sufficient conditions for such a subgroup to exist, study their existence under field extensions, and give some structural results describing the behaviour of maximal n-th root selection fields(original abstract)

Słowa kluczowe

EN

Mathematics; Mathematical functions; Mathematical statistics; Number theory

PL

Matematyka; Funkcje matematyczne; Statystyka matematyczna; Teoria liczb

• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2019
• Tom: 33
• Strony: 106--120

Twórcy

autor

Paweł Gładki

• Uniwersytet Śląski w Katowicach Instytut Matematyki

Bibliografia

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• P. Berrizbeitia, Additive properties of multiplicative subgroups of finite index in fields, Proc. Amer. Math. Soc. 112 (1991), 365-369.
• J. Königsmann, Half-ordered fields, PhD thesis, Universität Konstanz, Konstanz, 1993.
• T.Y. Lam, The theory of ordered fields, in: B.R. McDonald (ed.), Ring Theory and Algebra, III, Lecture Notes in Pure and Appl. Math., 55, Dekker, New York, 1980, pp. 1-152.
• T.Y. Lam, Introduction to Quadratic Forms over Fields, Graduate Studies in Mathematics, 67, American Mathematical Society, Providence, RI, 2005.
• L. Mahé, J. Mináč and T.L. Smith, Additive structure of multiplicative subgroups of fields and Galois theory, Doc. Math. 9 (2004), 301-355.
• E. Sperner, Die Ordnungsfunktionen einer Geometrie, Math. Ann. 121 (1949), 107-130.
• W.C. Waterhouse. Square root as a homomorphism, Amer. Math. Monthly 119 (2012), 235-239.

Identyfikatory

DOI

10.2478/amsil-2019-0012