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On M-Symmetric Lattices

Published online by Cambridge University Press:  20 November 2018

R. Padmanabhan
R. Padmanabhan*
Affiliation:
University of Manitoba, Winnipeg, Manitoba
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Every ⊥-symmetric relatively semi-orthocomplemented lattice is M-symmetric. This answers the Problem 1 in [2] in the affirmative and provides a new proof to a result on ⊥-symmetric lattices proved in [2] (Corollary below). The notation and terminology are as in [2].

Let 〈L; ⋀, V〉 be a lattice. Two elements a and b of L are said to form a modular pair, in symbols aMb, if

The relation aM✶b is defined dually.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 1 , 01 March 1974 , pp. 85 - 86
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Birkhoff, G., Lattice theory, 3rd ed., Colloq. Publ., Amer. Math. Soc, Providence, R.I., 1967.Google Scholar
2. Maeda, F. and Maeda, S.,Theory of symmetric lattices, Springer-Verlag, Berlin, 1970.Google Scholar