Nonassociative Galois rings

The aim of this paper is to introduce the notion of a generalised Galois ring, that is, a Galois ring without associativity assumptions. Some basic properties of associative Galois rings such as cardinality, characteristic, and ideal lattice structure are extended to the nonassociative case. An existence theorem for generalised Galois rings is also proved. However, the uniqueness results known in the associative case are not kept any longer for generalised Galois rings.
The research was partially supported by FEDER (IFD–97–0556), by MCYT (PB–PGI99–04), and by FICYT (PB–EXPO1–33)