For finite projective spaces of geometric dimension at least three, Wedderburn's little theorem implies that the division ring over which the projective space is defined must be a finite field, GF(q), whose order (that is, number of elements) is q (a prime power).
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In 1892, Gino Fano was the first to consider such a finite geometry – a three dimensional geometry containing 15 points, 35 lines, and 15 planes, with each plane containing 7 points and 7 lines.
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The first finite projective geometry was developed by the Italian mathematician Gino Fano.
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In projective geometry and finite geometry (MSC 51A, 51E, 12K10), a semifield is the analogue of a division algebra, but defined over the integers Z rather than over a field.