# Isomorphisms between Lattices of Linear Subspaces Which are Induced by Isometries

Chapter

## Abstract

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 ([1] p. 44) τ is induced by a semilinear map T: E → Ē if we assume that dim E ≥ 3.

## Keywords

Linear Subspace Lattice Versus Projective Geometry Division Ring Modular Lattice
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## References to Chapter IV

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