On strong automorphisms of direct products of Witt rings. Part 1

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

Abstrakty

EN

The notion of Witt ring is fundamental in bilinear algebra. Automorphisms of Witt rings have been investigated until recent years. In this paper we consider Witt rings which are direct products of finite number of other Witt rings. We shall present a necessary condition in order to group of all strong automorphisms of direct product of Witt rings be a direct product of groups of strong automorphisms of Witt rings which are factors in the direct product. Subsequently, there are considered some examples of Witt rings, where described condition is fulfilled.

Słowa kluczowe

EN

Witt rings; quaternionic structures; strong automorphisms

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2013
• Tom: Vol. 12, nr 3
• Strony: 123--133
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Stępień M. R.

• Chair of Mathematics, Kielce University of Technology Kielce, Poland

autor

Stępień L.

• Institute of Mathematics and Computer Science, Jan Długosz University Częstochowa, Poland

Bibliografia

• [1] Witt E., Teorie der quadratischen Formen in beliebigen Körpern, J. Reine Angew. Math. 1937, 176, 31-44.
• [2] Stępień M., Automorphisms of products of Witt rings of local type, Acta Mathematica et Informatica Universitatis Ostraviensis 2002, 10, 125-131.
• [3] 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.
• [4] Stępień M., Automorphisms of Witt Rings of Finite Fields, Scientific Issues. Mathematics, XVI, Jan Długosz University, Częstochowa 2011, 67-70.
• [5] Marshall M., Abstract Witt Rings, volume 57 of Queen's Papers in Pure and Applied Math., Queen's University, Ontario 1980.
• [6] Stępień M.R., Automorphisms of Witt rings and quaternionic structures, Scientific Research of the Institute of Mathematics and Computer Science, Częstochowa University of Technology 2011, 1(10), 231-237.
• [7] Lam T.Y., Introduction to Quadratic Forms over Fields, American Mathematics Society 2005, Graduate Studies in Mathematics 67.
• [8] Serre J.-P., A Course in Arithmetic, Springer-Verlag, New York-Heidelberg-Berlin 1973.
• [9] Stępień L., Stępień M.R., Automatic Search of Automorphisms of Witt Rings, Scientific Issues. Mathematics, XVI, Jan Długosz University, Częstochowa 2011, 141-146.