On the lattice of all closed subspaces of a Hermitian space

Hans Keller

Vol. 89 (1980), No. 1, 105–110

DOI: 10.2140/pjm.1980.89.105

Abstract

The purpose of the paper is to prove the following

Theorem: Let E be a vector space over a field K with char K≠2, and let ϕ be a nondegenerate hermitian form on E. Then the lattice of all orthogonally closed subspaces of (E,ϕ) is modular if and only if E is finite dimensional.

Mathematical Subject Classification 2000

Primary: 46C99

Secondary: 06C05, 15A63, 10C05

Milestones

Received: 10 May 1979

Published: 1 July 1980