Authors:
Sin-Ei Takahasi Laboratory of Mathematics and Games, Katsushika 2-371, Funabashi, Chiba 273-0032, Japan

Search for other papers by Sin-Ei Takahasi in
Current site
Google Scholar
PubMed
Close
,
Kiyoshi Shirayanagi Department of Information Science, Toho University, Miyama 2-2-1, Funabashi, Chiba 274-8510, Japan

Search for other papers by Kiyoshi Shirayanagi in
Current site
Google Scholar
PubMed
Close
, and
Makoto Tsukada Department of Information Science, Toho University, Miyama 2-2-1, Funabashi, Chiba 274-8510, Japan

Search for other papers by Makoto Tsukada in
Current site
Google Scholar
PubMed
Close
Open access

An endo-commutative algebra is a nonassociative algebra in which the square mapping preserves multiplication. In this paper, we give a complete classification of 2-dimensional endo-commutative straight algebras of rank one over an arbitrary non-trivial field, where a straight algebra of dimension 2 satisfies the condition that there exists an element x such that x and x2 are linearly independent. We list all multiplication tables of the algebras up to isomorphism.

  • [1]

    Ananin, A. and Mironov, A. The moduli space of 2-dimensional algebras. Comm. Algebra, 28, 9 (2000), 44814488.

  • [2]

    Asrorov, D., Bekbaev, U., and Rakhimov, I. A complete classification of two-dimensional endo-commutative algebras over an arbitrary field. arXiv:2304.00491v1 [math.RA] 2 Apr 2023.

    • Search Google Scholar
    • Export Citation
  • [3]

    Goze, M. and Remm, E. 2-dimensional algebras. Afr. J. Math. Phys. 10, 1 (2011), 8191.

  • [4]

    Kaygorodov, I. and Volkov, Y. The variety of 2-dimensional algebras over an algebraically closed field. Canad. J. Math. 71, 4 (2019), 819842.

    • Search Google Scholar
    • Export Citation
  • [5]

    Kaygorodov, I. and Volkov, Y. Complete classification of algebras of level two. Mosc. Math. J. 19, 3 (2019), 485521.

  • [6]

    Kobayashi, Y. Characterization of two-dimensional commutative algebras over a field of characteristic 2. Preprint (2016).

  • [7]

    Kobayashi, Y., Shirayanagi, K., Tsukada, M., and Takahasi, S.-E. A complete classification of three-dimensional algebras over ℝ and ℂ – OnkoChishin (visiting old, learn new). Asian-Eur. J. Math. 14, 8 (2021), Article ID 2150131 (25 pages).

    • Search Google Scholar
    • Export Citation
  • [8]

    Markova, O., Martínez, C., and Rodrigues, R. Algebras of length one. J. Pure Appl. Algebra 226, 7 (2022), Article ID 106993, 16 pp.

  • [9]

    Petersson, H. The classification of two-dimensional nonassociative algebras. Results Math. 37, 1-2 (2000), 120154.

  • [10]

    Takahasi, S.-E., Shirayanagi, K., and Tsukada, M. A classification of two-dimensional endo-commutative algebras over 𝔽2. arXiv:2211.04015v1 [math.RA] 8 Nov 2022.

    • Search Google Scholar
    • Export Citation
  • [11]

    Takahasi, S.-E., Shirayanagi, K., and Tsukada, M. A classification of endo-commutative curled algebras of dimension 2 over a non-trivial field. To appear in Asian-Eur. J. Math. 16–10 (2023), 2350191 (28 pages).

    • Search Google Scholar
    • Export Citation
  • Collapse
  • Expand
The Instruction for Authors is available in PDF format. Please, download the file from HERE.
Please, download the LaTeX template from HERE.

Editor in Chief: László TÓTH (University of Pécs)

Honorary Editors in Chief:

  • † István GYŐRI (University of Pannonia, Veszprém, Hungary)
  • János PINTZ (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)
  • Jörg THUSWALDNER (Montanuniversität Leoben, Leoben, Austria)
  • Zsolt TUZA (University of Pannonia, Veszprém, Hungary)

Advisory Board

  • Szilárd RÉVÉSZ (Rényi Institute of Mathematics, Budapest, Hungary)  - Chair
  • Gabriella BÖHM
  • György GÁT (University of Debrecen, Debrecen, Hungary)

University of Pécs,
Faculty of Sciences,
Institute of Mathematics and Informatics
Department of Mathematics
7624 Pécs, Ifjúság útja 6., HUNGARY
(36) 72-503-600 / 4179
ltoth@gamma.ttk.pte.hu

  • Mathematical Reviews
  • Zentralblatt
  • DOAJ

Publication Model Gold Open Access
Submission Fee none
Article Processing Charge 0 EUR/article (temporarily)
Subscription Information Gold Open Access

Mathematica Pannonica
Language English
Size A4
Year of
Foundation
1990
Volumes
per Year
1
Issues
per Year
2
Founder Akadémiai Kiadó
Founder's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Publisher Akadémiai Kiadó
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 2786-0752 (Online)
ISSN 0865-2090 (Print)