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

Stępień M. R.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2012

Vol. 11, nr 1

117-128

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.