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Automorphisms of Witt rings of local type

Stępień M. R.

Journal of Applied Mathematics and Computational Mechanics

2015

Vol. 14, nr 3

109-119

We present a description of the group of strong automorphisms of Witt rings of local type (Witt rings of local fields) using quaternionic structures.

Automorphisms of Witt rings of finite fields

Stępień M. R.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2011

Vol. 16

67--70

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.

Automorphisms of Witt rings and quaternionic structures

Stępień M. R.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2011

Vol. 10, nr 1

231-237

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.