Minimal Proper Quasifields with Additional Conditions

We investigate the finite semifields which are distributive quasifields, and finite near-fields which are associative quasifields. A quasifield Q is said to be a minimal proper quasifield if any of its sub-quasifield H ̸= Q is a subfield. It turns out that there exists a minimal proper near-field su...

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Bibliographic Details
Published in:Journal of Siberian Federal University. Mathematics & Physics 2020-01, Vol.13 (1), p.104-113
Main Author: Kravtsova, Olga V.
Format: Article
Language:English
Subjects:
Algorithms
Near fields
Prime numbers
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Summary:We investigate the finite semifields which are distributive quasifields, and finite near-fields which are associative quasifields. A quasifield Q is said to be a minimal proper quasifield if any of its sub-quasifield H ̸= Q is a subfield. It turns out that there exists a minimal proper near-field such that its multiplicative group is a Miller–Moreno group. We obtain an algorithm for constructing a minimal proper near-field with the number of maximal subfields greater than fixed natural number. Thus, we find the answer to the question: Does there exist an integer N such that the number of maximal subfields in arbitrary finite near-field is less than N? We prove that any semifield of order p4 (p be prime) is a minimal proper semifield
ISSN:1997-1397
2313-6022
DOI:10.17516/1997-1397-2020-13-1-104-113