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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Locally modular lattices and locally distributive lattices

Author: Shûichirô Maeda
Journal: Proc. Amer. Math. Soc. 44 (1974), 237-243
MSC: Primary 06A30
MathSciNet review: 0340132
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Abstract: A locally modular (resp. locally distributive) lattice is a lattice with a congruence relation and each of whose equivalence class has sufficiently many elements and is a modular (resp. distributive) sublattice. Both the lattice of all closed subspaces of a locally convex space and the lattice of projections of a locally finite von Neumann algebra are locally modular. The lattice of all $ {T_1}$-topologies of an infinite set is locally distributive.

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Keywords: Locally modular lattice, locally distributive lattice, semimodular, lattice of $ {T_1}$-topologies, standard element
Article copyright: © Copyright 1974 American Mathematical Society