Albert's Construction for Semifields of Even Order |
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| Authors: | G P Wene Irvin R Hentzel |
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| Institution: | 1. Department of Mathematics , The University of Texas at San Antonio , San Antonio, Texas, USA greg.wene@utsa.edu;3. Department of Mathematics , Iowa State University , Ames, Iowa, USA |
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| Abstract: | Albert's construction for commutative semifields of order 2 n , n odd, is presented. It avoids the construction of a presemifield and, in the case that n is prime, allows us to determine automorphism groups and the isomorphism classes. If n is a prime greater than three, the semifields are strictly not associative. These semifields are new for all n greater than three, differing from the binary semifields in that each admits only the trivial automorphism. The authors present an explicit construction of an isotope of the 25-element semifield that contains a subsemifield of order 22. |
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| Keywords: | Binary semifields Semifields Translation planes |
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