Warianty tytułu
Języki publikacji
Abstrakty
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)
Twórcy
autor
- Uniwersytet Śląski w Katowicach Instytut Matematyki
Bibliografia
- E. Becker, Hereditarily Pythagorean Fields and Orderings of Higher Level, Monografías de Matemática, 29, Instituto de Matemática Pura e Aplicada, Rio de Janeiro, 1978.
- E. Becker, Summen n-ter Potenzen in Körpern, J. Reine Angew. Math. 307/308 (1979), 8-30.
- 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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
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