- Tytuł:
- A construction of infinite set of rational self-equivalences
- Autorzy:
- Stępień, M.
- Powiązania:
- https://bibliotekanauki.pl/articles/121830.pdf
- Data publikacji:
- 2009
- Wydawca:
- Uniwersytet Humanistyczno-Przyrodniczy im. Jana Długosza w Częstochowie. Wydawnictwo Uczelniane
- Tematy:
-
pierścień Witta
symbol Legendre'a
twierdzenie Dirichleta
Witt rings
Legendre symbol
Dirichlet's theorem - Opis:
- In [5] it was shown that two number fields have isomorphic Witt rings of quadratic forms if and only if there is a Hilbert symbol equivalence between them. A Hilbert symbol equivalence between two number fields K and L is a pair of maps(t,T), where t: K ∗/K∗2→L∗/L∗2 is a group isomorpism and T: ΩK→Ω L is a bijection between the sets of finite and infinite primes of K and L, respectively, such that the Hilbert symbols are preserved: for any a; b∈K∗=K∗2and for any P∈ΩK,(a; b)P= (t(a), t(b))T(P) A Hilbert symbol equivalence between the field Q and itself is called rational self-equivalence. In [5] the authors present a construction of equivalence of two fields starting from the so called Hilbert small equivalence of two fields. We use this idea for constructing infinite set of rational self-equivalences.
- Źródło:
-
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics; 2009, 14; 117-132
2450-9302 - Pojawia się w:
- Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
- Dostawca treści:
- Biblioteka Nauki
Artykuł