Previous |  Up |  Next


Witt ring; orders in number fields; bilinear forms on ideals
We prove that there are infinitely many real quadratic number fields $K$ with the property that for infinitely many orders $\mathcal {O}$ in $K$ and for the maximal order $R$ in $K$ the natural homomorphism $\varphi :W\mathcal {O}\rightarrow WR$ of Witt rings is surjective.
[1] Ciemała M.: Natural homomorphisms of Witt rings of orders in algebraic number fields. Math. Slovaca 54 (2004), 473–477. MR 2114618
[2] Ciemała M., Szymiczek K.: On natural homomorphisms of Witt rings. Proc. Amer. Math. Soc. 133 (2005), 2519–2523. DOI 10.1090/S0002-9939-05-07896-2 | MR 2146193
[3] Ciemała M., Szymiczek K.: On injectivity of natural homomorphisms of Witt rings (submitted).
[4] Czogała A.: Generators of the Witt groups of algebraic integers. Ann. Math. Siles. 12 (1998), 105–121. MR 1673080
[5] Milnor J., Husemoller D.: Symmetric bilinear forms. Springer-Verlag, Berlin - Heidelberg - New York 1973. MR 0506372 | Zbl 0292.10016
[6] Neukirch J.: Algebraic number theory. Springer-Verlag, Berlin 1999. MR 1697859 | Zbl 0956.11021
[7] Sierpiński W.: Teoria Liczb. Monografie Matematyczne, Warszawa 1950. MR 0047060
[8] Ward M.: Prime divisors of second order recurring sequences. Duke Math. J. 21 (1954), 607–614). DOI 10.1215/S0012-7094-54-02163-8 | MR 0064073 | Zbl 0058.03701
Partner of
EuDML logo