On Lattice Complements
- 1 January 1965
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Glasgow Mathematical Association
- Vol. 7 (1) , 22-23
- https://doi.org/10.1017/s2040618500035103
Abstract
Let (L, ≦) be a distributive lattice with first element 0 and last element 1. If a, b in L have complements, then these must be unique, and the De Morgan laws provide complements for a ∧ b and a ∨ b. We show that the converse statement holds under weaker conditions.Theorem 1. If(L, ≦) is a modular lattice with 0 and 1 and if a, b in L are such that a ≦b and a ≨ b have (not necessarily unique) complements, then a andb have complements.Keywords
This publication has 2 references indexed in Scilit:
- Lattices With Unique ComplementsTransactions of the American Mathematical Society, 1945
- Lattices with unique complementsTransactions of the American Mathematical Society, 1945