On the axioms of quadratic form schemes
Abstract
We show that the generally accepted axioms C1, C2 and C3 of quadratic form schemes can be replaced by two simply axioms S1 and S2. Several operations on schemes and the notion of a complete scheme are introduced in the paper. A proof is given that every elementary scheme is complete.
References
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8. K. Szymiczek, Quadratic forms over fields with finite square class number, Acta Arith. 28 (1975), 195-221.
2. C. Cordes, The Witt group and the equivalence of fields with respect to quadratic forms, J. Algebra 26 (1973), 400-421.
3. C. Cordes, Quadratic forms over nonformally real fields with a finite number of quaternion algebras, Pacific J. Math. 63 (1976), 357-366.
4. M. Kula, Fields with prescribed quadratic form schemes. Math. Z. 167 (1979), 201-212.
5. M. Kula, Fields with non-trivial Kaplansky's radical and finite square class number. Acta Arith. 38 (1981), 411-418.
6. M. Kula, L. Szczepanik, K. Szymiczek, Quadratic forms over formally real fields with eight square classes, Manuscripta Math. 29 (1979), 295-303.
7. L. Szczepanik, Klasyfikacja pierścieni Witta w aksjomatycznej teorii form kwadratowych. Praca doktorska, Uniwersytet Śląski, Katowice 1979.
8. K. Szymiczek, Quadratic forms over fields with finite square class number, Acta Arith. 28 (1975), 195-221.
PękałaJ. G. (1990). On the axioms of quadratic form schemes. Annales Mathematicae Silesianae, 3, 24-31. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14298
Jan. G. Pękała
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
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