Abstract
It is proved that a minimal generating system of the lattice of all subspaces of a finite-dimensional vector space over a finite field of q elements contains at most max(q+3) elements. This bound does not depend on the dimension of the space.
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 114, pp. 148–149, 1982.
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Kravchenko, A.A. Minimal number of generators of the lattice of subspaces of a finite-dimensional linear space. J Math Sci 27, 2942–2943 (1984). https://doi.org/10.1007/BF01410747
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DOI: https://doi.org/10.1007/BF01410747