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 k̄ and τ: 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
- R. Baer, Linear Algebra and Projective Geometry. Academic Press, New York 1952.Google Scholar
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