Spread-Theoretic Dual of a Semifield


Given a finite pre-semifield (S,+,\circ ), the dual pre-semifield %(S,+,\ast ) has multiplication a\ast b=b\circ a. In this article, acharacterization is given of the dual pre-semifield in terms of theassociated spreads. This is then used to give a new proof that shows thatself-dual pre-semifield spreads when transposed and dualized constructself-transpose semifield spreads. When the self-dual pre-semifield isactually commutative then the transpose-dual spread is symplectic. We alsogive a spread-only description of the six semifields arising from a givensemifield.

DOI Code: 10.1285/i15900932v29n1p145

51E23; 51A40

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