Cubic surfaces in AG(3,q) and projective planes of order \(q^ 3\) (Q920396)
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scientific article; zbMATH DE number 4163620
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Cubic surfaces in AG(3,q) and projective planes of order \(q^ 3\) |
scientific article; zbMATH DE number 4163620 |
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Cubic surfaces in AG(3,q) and projective planes of order \(q^ 3\) (English)
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1990
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The author determines all cubic surfaces in the affine 3-space AG(3,q). This leads to a complete classification of the semifield planes of order \(q^ 3\) whose spread sets are division algebras of dimension 3. As a corollary follows a result of Menichetti that finite division algebras of dimension 3 are associative or are twisted fields. This paper is an extension of a recent paper of the author [Can. J. Math. 38, 672-696 (1986; Zbl 0601.51008)].
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division algebra
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cubic surfaces in AG(3,q)
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