Natural homomorphisms of Witt rings of orders in algebraic number fields. II

Marzena Ciemała

Acta Mathematica Universitatis Ostraviensis (2006)

  • Volume: 14, Issue: 1, page 13-16
  • ISSN: 1804-1388

Abstract

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We prove that there are infinitely many real quadratic number fields K with the property that for infinitely many orders 𝒪 in K and for the maximal order R in K the natural homomorphism ϕ : W 𝒪 W R of Witt rings is surjective.

How to cite

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Ciemała, Marzena. "Natural homomorphisms of Witt rings of orders in algebraic number fields. II." Acta Mathematica Universitatis Ostraviensis 14.1 (2006): 13-16. <http://eudml.org/doc/35156>.

@article{Ciemała2006,
abstract = {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.},
author = {Ciemała, Marzena},
journal = {Acta Mathematica Universitatis Ostraviensis},
keywords = {Witt ring; orders in number fields; bilinear forms on ideals},
language = {eng},
number = {1},
pages = {13-16},
publisher = {University of Ostrava},
title = {Natural homomorphisms of Witt rings of orders in algebraic number fields. II},
url = {http://eudml.org/doc/35156},
volume = {14},
year = {2006},
}

TY - JOUR
AU - Ciemała, Marzena
TI - Natural homomorphisms of Witt rings of orders in algebraic number fields. II
JO - Acta Mathematica Universitatis Ostraviensis
PY - 2006
PB - University of Ostrava
VL - 14
IS - 1
SP - 13
EP - 16
AB - 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.
LA - eng
KW - Witt ring; orders in number fields; bilinear forms on ideals
UR - http://eudml.org/doc/35156
ER -

References

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  1. Ciemała M., Natural homomorphisms of Witt rings of orders in algebraic number fields, . Math. Slovaca 54 (2004), 473–477. MR2114618
  2. Ciemała M., Szymiczek K., 10.1090/S0002-9939-05-07896-2, . Proc. Amer. Math. Soc. 133 (2005), 2519–2523. MR2146193DOI10.1090/S0002-9939-05-07896-2
  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. (1998) MR1673080
  5. Milnor J., Husemoller D., Symmetric bilinear forms, . Springer-Verlag, Berlin - Heidelberg - New York 1973. (1973) Zbl0292.10016MR0506372
  6. Neukirch J., Algebraic number theory, . Springer-Verlag, Berlin 1999. (1999) Zbl0956.11021MR1697859
  7. Sierpiński W., Teoria Liczb, . Monografie Matematyczne, Warszawa 1950. (1950) MR0047060
  8. Ward M., 10.1215/S0012-7094-54-02163-8, . Duke Math. J. 21 (1954), 607–614). (1954) Zbl0058.03701MR0064073DOI10.1215/S0012-7094-54-02163-8

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