Mathematics

Automorphisms of residue rings of integer rings of circular fields

A. V. Shponko

South Ural State University

Abstract: The authors research the structure of residue rings of integer rings of circular fields by analyzing their ring automorphisms. The connections between a special subgroup of the automorphism group and the system of the inserted subrings of the residue rings are found. Among the occurring subrings the authors found a very prospective one for further research as well as a multitude of its noninvertible elements for some nontrivial cases.

Keywords: Abelian fields, circular fields, integer rings, residue rings, subrings, automorphisms.

UDC: 511.625

Received: 13.07.2011