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The Characterization of a Lattice Homomorphism

Published online by Cambridge University Press:  20 November 2018

Jongsik Kim
Jongsik Kim*
Affiliation:
National University, Seoul, Korea
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We shall give a simple characterization of a lattice homomorphism from a linear lattice E to a linear lattice F. This paper is motivated by the following two theorems in Kaplan [2] :

If ϕ is a lattice homomorphism, then ϕt(Fb) is an ideal in Eb.

(2) If ϕ is a lattice homomorphism, then ϕtt is a lattice homomorphism from ϕbb into ϕbb.

The main theorem is stated and proved in section 3. In section 1, we shall give notations and in section 2, we shall prove a main lemma. For details, we refer to Vulikh [3].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 1 , 01 February 1975 , pp. 172 - 175
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Kaplan, S., The second dual of the space of continuous functions. II, Trans. Amer. Math. Soc. 93 (1959), 329–350.Google Scholar
2. Kaplan, S., The second dual of the space of continuous functions. V, Trans. Amer. Math. Soc. 118 (1964), 512–546.Google Scholar
3. Vulikh, B., Introduction to the theory of partially ordered spaces (Wolters-Noordhoff Scientific Pub. Ltd., 1967).Google Scholar