Mathematica Pannonica
Volume/Issue:
Volume 27_NS1: Issue 2
From Binary Groups to Terminal Rings
Author:
Stuart D. Scott Department of Mathematics, University of Auckland, Auckland, New Zealand

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Pages:
125–151
Online Publication Date:
08 Oct 2021
Publication Date:
18 Nov 2021
Article Category:
Research Article
DOI:
https://doi.org/10.1556/314.2021.00013
Keywords:
nearring; binary group; anti-associative ring; anti-commutative ring; inverse ring; terminal ring
Open access

Binary groups are a meaningful step up from non-associative rings and nearrings. It makes sense to study them in terms of their nearrings of zero-fixing polynomial maps. As this involves algebras of a more specialized nature these are looked into in sections three and four. One of the main theorems of this paper occurs in section five where it is shown that a binary group V is a P0(V) ring module if, and only if, it is a rather restricted form of non-associative ring. Properties of these non-associative rings (called terminal rings) are investigated in sections six and seven. The finite case is of special interest since here terminal rings of odd order really are quite restricted. Sections eight to thirteen are taken up with the study of terminal rings of order pn (p an odd prime and n ≥ 1 an integer ≤ 7).

  • [1]

    E. Aichinger. Congruence lattices forcing nilpotency. J. Algebra Appl., 17(2):1850033, 2018.

  • [2]

    P. Higgins. Groups with multiple operations. Proc. Lon. Math. Soc., 6(3):366–416, 1956.

  • [3]

    H. Neumann. Varieties of groups and their associated nearrings. Math. Z., 65:36–69, 1956.

  • [4]

    G. Pitz. Nearrings. Revised Edition. North-Holland. Amsterdam (1983)

  • [5]

    R. Schafer. An introduction to non-associative algebras. Academic Press, New York (1966)

  • [6]

    S. Scott. Binary groups, 1–137, 2019. Manuscript.

  • [7]

    S. Scott. N-solubility and N-nilpotency in tame N-groups. Alg. Coll., 5(4):425–448, 1998.

  • [8]

    S. Scott. Tame nearrings and N-groups. Proc. Edin. Math. Soc., 23:275–296, 1980.

  • [9]

    S. Scott. The structure of Ω-groups. Nearrings, nearfields and K -loops, Kluever Acad. Pub., Netherlands, 1997, 47–137.

  • [10]

    S. Scott. The Z -constrained conjecture. Nearrings and Nearfields. Hamburg, 2003, 69–168. Springer, Dordrecht, 2005.

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Cover Mathematica Pannonica
Mathematica Pannonica
Print ISSN:
0865-2090
Online ISSN:
2786-0752

Editor in Chief: László TÓTH, University of Pécs, Pécs, Hungary

Honorary Editors in Chief:

  • János PINTZ, HUN-REN Alfréd Rényi Institute of Mathematics, Budapest, Hungary
  • † Ferenc SCHIPP, Eötvös Loránd University, Budapest, Hungary and University of Pécs, Pécs, Hungary
  • Sándor SZABÓ, University of Pécs, Pécs, Hungary
     

Deputy Editors in Chief:

  • Erhard AICHINGER, JKU Linz, Linz, Austria
  • Ferenc HARTUNG, University of Pannonia, Veszprém, Hungary
  • Ferenc WEISZ, Eötvös Loránd University, Budapest, Hungary

Editorial Board

  • Attila BÉRCZES, University of Debrecen, Debrecen, Hungary
  • István BERKES, Rényi Institute of Mathematics, Budapest, Hungary
  • Károly BEZDEK, University of Calgary, Calgary, Canada
  • György DÓSA, University of Pannonia, Veszprém, Hungary
  • Balázs KIRÁLY – Managing Editor, University of Pécs, Pécs, Hungary
  • Vedran KRCADINAC, University of Zagreb, Zagreb, Croatia 
  • Željka MILIN ŠIPUŠ, University of Zagreb, Zagreb, Croatia
  • Gábor NYUL, University of Debrecen, Debrecen, Hungary
  • Margit PAP, University of Pécs, Pécs, Hungary
  • István PINK, University of Debrecen, Debrecen, Hungary
  • Mihály PITUK, University of Pannonia, Veszprém, Hungary
  • Lukas SPIEGELHOFER, Montanuniversität Leoben, Leoben, Austria
  • Andrea ŠVOB, University of Rijeka, Rijeka, Croatia
  • Csaba SZÁNTÓ, Babeş-Bolyai University, Cluj-Napoca, Romania
  • Jörg THUSWALDNER, Montanuniversität Leoben, Leoben, Austria
  • Zsolt TUZA, University of Pannonia, Veszprém, Hungary

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  • György GÁT, University of Debrecen, Debrecen, Hungary

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Mathematica Pannonica
Language English
Size A4
Year of
Foundation		 1990
Volumes
per Year		 1
Issues
per Year		 2
Founder Akadémiai Kiadó
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ISSN 2786-0752 (Online)
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