Automorphisms of Witt rings and quaternionic structures

• Autorzy: Stępień M. R.
• Języki publikacji: EN

Abstrakty

EN

M. Marshall introduced the notion of quaternionic structure and he showed that the categories of Witt rings and quaternionic structures are naturally equivalent. Quaternionic structures turn out to bea useful tool for the investigation of Witt rings, since it suffices to handle the structure of a group. In our paper we shall describe precisely the one-to-one correspondence between automorphisms of quaternionic structures and strong the automorphisms of Witt rings.

Słowa kluczowe

EN

Witt ring; automorphisms; quaternionic structures

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
• Rocznik: 2011
• Tom: Vol. 10, nr 1
• Strony: 231--237
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Stępień M. R.

• Kielce University of Technology,

Bibliografia

• [1] Witt E., Theorie de quadratishen Formen in beliebigen Körpern, J. Reine Angew. Math. 1937, 176, 31-44.
• [2] Pfister A., Zur Darstellung von -1 als Summe von Quadraten in einem Körper, J. London Math. Soc. 1965, 40, 159-165.
• [3] Pfister A., Quadratishe Formen in beliebigen Körpern. Invent. Math. 1966, 1,116-132.
• [4] Pfister A., Zur Darstellung definiter Funktionen als Summe von Quadraten, Invent. Math. 1967, 4, 229-237.
• [5] Szymiczek K., Bilinear Algebra: An Introduction to the Algebraic Theory of Quadratic Forms, Algebra, Logic and Applications Series, Vol. 7, Gordon and Breach Science Publishers, Amsterdam 1997.
• [6] Lam T.Y., Introduction to Quadratic Forms over Fields, Graduate Studies in Mathematics, vol. 67, American Mathematics Society 2005.
• [7] Marshall M., Abstract Witt Rings, Volume 57 of Queen's Papers in Pure and Applied Math. Queen's University, Ontario 1980.
• [8] Stępień M., Automorphisms of products of Witt rings of local type, Acta Mathematica et Informatica Universitatis Ostraviensis 2002, 10, 125-131.
• [9] Stępień M., Automorphisms of Witt rings of elementary type, Mathematica. Proceedings of the XIth Slovak-Polish-Czech Mathematical School, Pedagogical Faculty Catholic University in Ružomberok, June 2nd - 5th, 2004, 62-67.
• [10] Stępień M.R., Automorphisms of Witt rings of finite fields, Scientific Issues, Mathematics, XVI, Jan Długosz University, Częstochowa 2011, 67-70.