Abstract
A Generalized Galois Ring (GGR) S is a finite nonassociative ring with identity of characteristic pn, for a prime number p, such that its top-factor S̄ = S/pS is a finite semifield. It is well known that if S is an associative Galois Ring (GR) then the set S* = S \ pS is a finite multiplicative abelian group. This group is cyclic if and only if S is either a finite field, or a residual integer ring_of odd characteristic or the ring ℤ4. A GGR is called top-associative if S̄ is a finite field. In this paper we study the conditions for a top-associative not associative GGR S to be cyclic. © Springer-Verlag Berlin Heidelberg 2004.
Cite
CITATION STYLE
González, S., Markov, V. T., Martínez, C., Nechaev, A. A., & Rúa, I. F. (2004). On cyclic top-associative generalized Galois rings. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2948, 25–39. https://doi.org/10.1007/978-3-540-24633-6_3
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