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AIMS Mathematics

2020, Volume 5, Issue 6: 6552-6579. doi: 10.3934/math.2020422
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Research article

Advanced results in enumeration of hyperfields

  • 1.
    School of Mathematics, Statistic and Computer Sciences, University of Tehran, Tehran, Iran
  • 2.
    Department of Mathematics and Physics, University of Defence in Brno, Czech Republic
  • Received: 04 June 2020 Accepted: 06 July 2020 Published: 24 August 2020

  • MSC : 20N20

  • The purpose of this paper is to introducing a computational method to construction and classification of finite hyperfields (in the sense of Krasner). In this regards first we introduce a mathematical method to produce hyperfields from a family of a non-empty subsets of a given multiplicative group under specific conditions and then we apply this method to enumerate all finite hyperfields of order less that 7, up to isomorphism by a computer programming. Of course this program can be used to produce hyperfields of finite higher orders, but it's commotional complexity is of high order and it must be used of very high-speed computers system.

    Citation: R. Ameri, M. Eyvazi, S. Hoskova-Mayerova. Advanced results in enumeration of hyperfields[J]. AIMS Mathematics, 2020, 5(6): 6552-6579. doi: 10.3934/math.2020422

    Related Papers:

  • The purpose of this paper is to introducing a computational method to construction and classification of finite hyperfields (in the sense of Krasner). In this regards first we introduce a mathematical method to produce hyperfields from a family of a non-empty subsets of a given multiplicative group under specific conditions and then we apply this method to enumerate all finite hyperfields of order less that 7, up to isomorphism by a computer programming. Of course this program can be used to produce hyperfields of finite higher orders, but it's commotional complexity is of high order and it must be used of very high-speed computers system.


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