Uncountability of the group of strong automorphisms of Witt ring of rational numbers

• Autorzy: Stępień M. R.
• Języki publikacji: EN

Abstrakty

EN

We use the notion of rational self-equivalence which is a special case of Hilbert symbol equivalence of fields, where both fields are considered to be the field Q of rational numbers. We define a small self-equivalence of the field Q as a special case of small equivalence of fields - a tool for constructing Hilbert-symbol equivalence of fields. We shall show, that one can choose initial sets of prime numbers and then control the processes of extending of small self-equivalence such that uncountable many rational self-equivalences can be constructed. The final conclusion is the corollary deciding that the group of strong automorphisms of Witt ring W(Q) of rational numbers is uncountable.

Słowa kluczowe

EN

Hilbert symbol; field theory

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
• Rocznik: 2012
• Tom: Vol. 11, nr 1
• Strony: 117--128
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Stępień M. R.

• Kielce University of Technology, Poland,

Bibliografia

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• [2] Czogała A., Hilbert-symbol equivalence of global fields, Prace Naukowe Uniwersytetu Śląskiego w Katowicach vol. 1969, Wyd. Uniwersytetu Śląskiego, Katowice 2001 (in Polish).
• [3] Czogała A., Hilbert-symbol equivalence of global function fields, Mathematica Slovaca 2001, 51, 4, 383-401.
• [4] Browkin J., Field theory, Biblioteka Matematyczna 49, PWN, Warsaw 1978 (in Polish).
• [5] Cassels J.W.S., Fröhlich A. (ed.), Algebraic Number Theory, Academic Press, London, New York 1967.
• [6] Serre J.-P., A Course in Arithmetic, Springer-Verlag, New York, Heidelberg, Berlin 1973.
• [7] Stępień M., A construction of infinite set of rational self-equivalences, Scientific Issues. Mathematics, XIV: 117-132, Jan Długosz University, Częstochowa 2009.
• [8] Marshall M., Abstract Witt Rings, volume 57 of Queen's Papers in Pure and Applied Math. Queen's University, Ontario 1980.
• [9] Stępień M. R., Automorphisms of Witt rings and quaternionic structures, Scientific Research of the Institute of Mathematics and Computer Science Częstochowa University of Technology 2011, 1(10), 231-237.