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Nonassociative Galois rings. (English. Russian original) Zbl 1134.17303
Discrete Math. Appl. 12, No. 6, 591-606 (2002); translation from Diskretn. Mat. 14, No. 4, 117-132 (2002).
Summary: The aim of this paper is to introduce the notion of a generalized 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 generalized Galois rings is also proved. However, the uniqueness results known in the associative case are not kept any longer for generalized Galois rings.

MSC:
17A60 Structure theory for nonassociative algebras
17A35 Nonassociative division algebras
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