Journal of Siberian Federal University. Mathematics & Physics / Minimal Proper Quasifields with Additional Conditions

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Journal of Siberian Federal University. Mathematics & Physics. 2020 13 (1)
Kravtsova, Olga V.
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Kravtsova, Olga V.: Siberian Federal University Krasnoyarsk, Russian Federation; ; OCRID: 0000-0002-6005-2393
quasifield; semifield; near-field; subfield

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

Paper at repository of SibFU