| Abstract: | It is proved that the minimum number of generators of the lattice of all subspaces of a finite-dimensional vector space over a field is finite if and only if the field is finitely generated over the prime field. An upper bound is given for this number, which does not depend on the dimension of the space and is linearly dependent on the number of elements generating the field.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 132, pp. 110–113, 1983. |
