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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.

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

Stępień M. R., Stępień L.

Journal of Applied Mathematics and Computational Mechanics

2013

Vol. 12, nr 3

123--133

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.

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.

A Clifford-type structure

Królikowski W.

Demonstratio Mathematica

2003

Vol. 36, nr 3

563--578