Composition of quaternary quadratic forms

M. Kneser; M.-A. Knus; M. Ojanguren; R. Parimala; R. Sridharan

Compositio Mathematica (1986)

  • Volume: 60, Issue: 2, page 133-150
  • ISSN: 0010-437X

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Kneser, M., et al. "Composition of quaternary quadratic forms." Compositio Mathematica 60.2 (1986): 133-150. <http://eudml.org/doc/89801>.

@article{Kneser1986,
author = {Kneser, M., Knus, M.-A., Ojanguren, M., Parimala, R., Sridharan, R.},
journal = {Compositio Mathematica},
keywords = {Arf invariant; composition of quaternary quadratic forms; Clifford algebra; quaternion algebra; groupoid; quadratic modules},
language = {eng},
number = {2},
pages = {133-150},
publisher = {Martinus Nijhoff Publishers},
title = {Composition of quaternary quadratic forms},
url = {http://eudml.org/doc/89801},
volume = {60},
year = {1986},
}

TY - JOUR
AU - Kneser, M.
AU - Knus, M.-A.
AU - Ojanguren, M.
AU - Parimala, R.
AU - Sridharan, R.
TI - Composition of quaternary quadratic forms
JO - Compositio Mathematica
PY - 1986
PB - Martinus Nijhoff Publishers
VL - 60
IS - 2
SP - 133
EP - 150
LA - eng
KW - Arf invariant; composition of quaternary quadratic forms; Clifford algebra; quaternion algebra; groupoid; quadratic modules
UR - http://eudml.org/doc/89801
ER -

References

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  2. [BS] F. Van Der Blij and T.A. Springer: The arithmetic of octaves and of the group G2. Indag. Math.21 (1959) 406-418. Zbl0089.25803MR152555
  3. [Br 1] H. Brandt: Zur Komposition der quaternären quadratischen Formen. J. reine angew. Math.143 (1913) 106-129. Zbl44.0253.02JFM44.0253.02
  4. [Br 2] H. Brandt: Der Kompositionsbegriff bei den quaternären quadratischen Formen. Math. Ann.91 (1924) 300-315. Zbl50.0099.01MR1512195JFM50.0099.01
  5. [Br 3] H. Brandt: Idealtheorie in Quaternionenalgebren. Math. Ann.99 (1928) 1-29. MR1512436JFM54.0163.01
  6. [Brz 1] J. Brzezinski: A characterization of Gorenstein orders in quaternion algebras. Math. Scand.50 (1982) 19-24. Zbl0483.16002MR664504
  7. [Brz 2] J. Brzezinski: On orders in quaternion algebras. Communications in Algebra11 (1983) 501-522. Zbl0517.16006MR693798
  8. [Ka] I. Kaplansky: Submodules of quaternion algebras. Proc. London Math. Soc.19 (1969) 219-232. Zbl0212.39102MR240142
  9. [Kn] M. Kneser: Composition of binary quadratic forms. J. Number Theory15 (1982) 406-413. Zbl0493.10029MR680541
  10. [Kö] O. Körner: Ordnungen von Quaternionenalgebren über lokalen Körpern. J. reine angew. Math.333 (1982) 162-178. Zbl0477.12020MR660789
  11. [KP] M.-A. Knus and A. Paques: Quadratic spaces with trivial Arf invariant. J. of Algebra93 (1985) 267-291. Zbl0625.16003MR786754
  12. [N] M. Nagata: Local Rings. R.E. Krieger Publishing Comp.: New York (1975). Zbl0386.13010MR460307
  13. [P] P. Ponomarev: Class numbers of definite quaternary forms with square discriminant. J. Number Theory6 (1974) 291-317. Zbl0294.10015MR347733

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