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International Conference on Finite Fields and Applications

Fq 2003: Finite Fields and Applications pp 25–39Cite as

On Cyclic Top-Associative Generalized Galois Rings

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2948))

Abstract

A Generalized Galois Ring (GGR) S is a finite nonassociative ring with identity of characteristic p n, for a prime number p, such that its top-factor \(\overline{S} = S/pS\) 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 \(\overline{S}\) is a finite field. In this paper we study the conditions for a top-associative not associative GGR S to be cyclic.

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Author information

Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Oviedo, 33007, Oviedo, Spain

    Santos González, Consuelo Martínez & Ignacio F. Rúa

  2. Center of New Information Technologies, Moscow State University, 119899, Moscow, Russia

    Viktor T. Markov & Aleksandr A. Nechaev

Authors
  1. Santos González
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  2. Viktor T. Markov
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  3. Consuelo Martínez
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  4. Aleksandr A. Nechaev
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  5. Ignacio F. Rúa
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Editor information

Editors and Affiliations

  1. Department of Mathematics, The Pennsylvania State University, University Park, 16802, PA, USA

    Gary L. Mullen

  2. University Paul Sabatier, AAECC/IRIT, 118 route de Narbonne, 31300, Toulouse cedex, France

    Alain Poli

  3. Sabancı University - FENS, Orhanli - Tuzla, 34956, Istanbul, Turkey

    Henning Stichtenoth

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© 2004 Springer-Verlag Berlin Heidelberg

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González, S., Markov, V.T., Martínez, C., Nechaev, A.A., Rúa, I.F. (2004). On Cyclic Top-Associative Generalized Galois Rings. In: Mullen, G.L., Poli, A., Stichtenoth, H. (eds) Finite Fields and Applications. Fq 2003. Lecture Notes in Computer Science, vol 2948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24633-6_3

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  • DOI: https://doi.org/10.1007/978-3-540-24633-6_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21324-6

  • Online ISBN: 978-3-540-24633-6

  • eBook Packages: Springer Book Archive

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