New Semifield Planes of order 81

Mathematics – Rings and Algebras

Scientific paper

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14 pages. Revised paper (original title: New semifield planes of orders 64 and 81). U. Dempwolff had previously and independen

Scientific paper

A finite semifield is a finite nonassociative ring with identity such that the set of its nonzero elements is closed under the product. From any finite semifield a projective plane can be constructed. In this paper we obtain new semifield planes of orders 81 by means of computational methods. These computer-assisted results yield to a complete classification (up to isotopy) of 81-element finite semifields.

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