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On strong automorphisms of direct products of Witt rings. Part 2

Stępień M. R., Stępień L.

Journal of Applied Mathematics and Computational Mechanics

2013

Vol. 12, nr 4

119--125

In the paper strong automorphisms of finitely generated Witt rings are considered. Every finitely generated Witt ring can be expressed in terms of Z / 2Z and basic indecomposable Witt rings using the operations of group ring formation and direct product. Groups of strong automorphisms of basic indecomposables and their direct products and the description of all strong automorphisms of any group Witt ring are known. In this paper the strong automorphisms of direct products of group Witt rings are considered. Presented are two wide classes of Witt rings where the group of strong automorphisms is isomorphic to the direct product of groups of strong automorphisms of Witt rings which are factors in the direct product.

Ulm-Kaplansky invariants of S(KG)/G

Danchev P. V.

Bulletin of the Polish Academy of Sciences. Mathematics

2005

Vol. 53, no 2

147-156

Let G be an infinite abelian p-group and let K be a field of the first kind with respect to p of characteristic different from p such that sp(K) = N or sp (K) = N∪{0}. The main result of the paper is the computation of the Ulm–Kaplansky functions of the factor group S(KG)/G of the normalized Sylow p-subgroup S(KG) in the group ring KG modulo G. We also characterize the basic subgroups of S(KG)/G by proving that they are isomorphic to S(KB)/B, where B is a basic subgroup of G.