Minimal proper quasifields with additional conditions


Тип публикации: статья из журнала

Год издания: 2020

Идентификатор DOI: 10.17516/1997-1397-2020-13-1-104-113

Ключевые слова: Near-field, Quasifield, Semifield, Subfield

Аннотация: 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 iПоказать полностьюs 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. © Siberian Federal University. All rights reserved.

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Журнал: Journal of Siberian Federal University - Mathematics and Physics

Выпуск журнала: Vol. 13, Is. 1

Номера страниц: 104-113

ISSN журнала: 19971397