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Some Homological Pathology in Vector Lattices

Published online by Cambridge University Press:  20 November 2018

David M. Topping
David M. Topping*
Affiliation:
The University of Chicago
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The purpose of this paper is to point out a number of curious phenomena in the category of (real) vector lattices and linear lattice homomorphisms. Birkhoff (3, p. 221, Ex. 2 and Problem 96) called attention to the question of constructing models of the free objects with more than one generator in this category, a problem recently solved by E. C. Weinberg (9). In §6 we construct a more manageable class of (non-free) projective vector lattices. Here, however, there is a countability restriction which suggests strong connections with free and projective Boolean algebras (in the category of Boolean algebras and their homomorphisms, such algebras must satisfy the countable chain condition (6)).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 411 - 428
Copyright
Copyright © Canadian Mathematical Society 1965

References

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