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Symmetric Lattices and Basic Properties of Lattices 1 Modularity in Lattices
Semiorthogonality in Lattices
Semiorthogonality in 1Symmetric Lattices
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affine matroid lattice assume atomistic Wilcox lattice Baer ring Baer semigroup bl^b called central element closed subspace complete lattice contains a third continuous linear form contradiction Corollary covering property Definition denote division ring dual spaces dual-atom dual-atomistic Euclid's strong parallel Evidently exchange property Exercise exist atoms exists an atom exists an element finite element finite subset finite-modular AC-lattice following condition following three statements Frechet space Hence imaginary unit incomplete element irregular element isomorphic LC(E left complemented Lemma locally convex space M-symmetric Maeda mapping modular element modular lattice modular matroid lattice Moreover non-zero element orthocomplemented lattice orthomodular lattice Proof prove relatively complemented lattice Remark resp satisfies the following semi-orthogonal family singular element statements are equivalent strong parallel axiom strongly planar sublattice subperspective Symmetric Lattices take a point Theorem topological vector space topology upper continuous weakly modular whence Z-lattice