Isomorphisms between Lattices of Linear Subspaces Which are Induced by Isometries
Let E be a vector space over the division ring k and L(E) the lattice of all linear subspaces of E. If Ē is a vector space over the division ring k and T: L(E); → L(Ē) a lattice isomorphism then by the Fundamental Theorem of Projective Geometry ( p. 44) τ is induced by a semilinear map T: E → Ē if we assume that dim E ≥ 3.
KeywordsLinear Subspace Lattice Versus Projective Geometry Division Ring Modular Lattice
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References to Chapter IV
- C. Herrmann, On a condition sufficient for the distributivity of lattices of linear subspaces. To appear.Google Scholar
- P. Pudlak and J. Túma, Yeast graphs and fermentation of algebraic lattices. Coll. Math. Soc. J. Bolyai, 14 (1976) Lattice Theory 301–342 ed. by A.P. Huhn and E.T. Schmidt, North Holland Publ. Company, Amsterdam.Google Scholar