Automorphisms of Witt rings of finite fields

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

Abstrakty

EN

The problem of general description of the group of automorphisms of any Witt ring W seems to be very difficult to solve. However, there are many types of Witt rings, which automorphism are described precisely (e.g. [1], [2], [4], [5], [6],[7], [8]). In our paper we characterize automorphisms of abstract Witt rings (cf. [3]) isomorphic to powers of Witt rings of quadratic forms with coefficients in finite fields with characteristic different from 2.

Słowa kluczowe

EN

Witt ring; automorphisms; automorphisms of Witt rings; automorphism group

PL

pierścień Witta; automorfizm; automorfizm pierścieni Witta; grupa automorfizmów

• Wydawca: Wydawnictwo Uniwersytetu Humanistyczno-Przyrodniczego im. Jana Długosza w Częstochowie
• Czasopismo: Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
• Rocznik: 2011
• Tom: Vol. 16
• Strony: 67--70
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Stępień M. R.

• Kielce University of Technology al. Tysiąclecia Państwa Polskiego 7, 25-314 Kielce, Poland

Bibliografia

• [1] R. Baeza, R. Moresi. On the Witt-equivalence of fields of characteristic 2. Journal of Algebra, 92, 446-453, 1985.
• [2] A. Czogała. On reciprocity equivalence of quadratic number fields. Acta Arithmetica, 58, No. 1, 27-46, 1981.
• [3] M. Marshall. Abstract Witt Rings. Queen's Papers in Pure and Applied Math., 57, Queen's University, Ontario 1980.
• [4] R. Perlis, K. Szymiczek, P.E. Conner, R. Litherland. Matching Witts with global fields. In: W.B. Jacob, T.-Y. Lam, R.O. Robson (Eds.), Recent Advances in Real Algebraic Geometry and Quadratic Forms, (Proceedings of the RAGSQUAD Year, Berkeley 1990-1991), Contemporary Mathematics, 155, 365-387, Amer. Math. Soc. Providence, Rhode Island 1994.
• [5] M. Stępień. Automorphisms of products of Witt rings of local type. Acta Mathematica et Informatica Universitatis Ostraviensis, 10, 125-131, 2002.
• [6] M. Stępień. Automorphisms of Witt rings of elementary type. Mathematica. Proc. XIth Slovak-Polish-Czech Mathematical School, Catholic University in Ruzomberok, 10, 62-67, 2004.
• [7] M. Stępień. A construction of infinite set of rational self-equivalences. Scientific Issues, Jan Długosz University in Częstochowa, Mathematics, XIV, 117-132, 2009.
• [8] R. Ware. Automorphisms of Pythagorean fields and their Witt rings. Commutative Algebra, 17, No. 4, 945-969, 1989.