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Applications of Duality in the Theory of Finitely Generated Lattice-Ordered Abelian Groups

Published online by Cambridge University Press:  20 November 2018

W. M. Beynon
W. M. Beynon*
Affiliation:
University of Warwick, Coventry, England
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Abstract

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In a previous paper by the author [3], duality theorems for finitely generated vector lattices and lattice-ordered Abelian groups are described. In particular, the category of finitely generated semi-simple vector lattices is shown to be equivalent to a geometrical category V whose objects are topologically closed cones in Euclidean space, and whose morphisms, called ll-maps\ form a special subclass of the class of piece wise homogeneous linear maps between such cones. Under this categorical duality, finitely generated projective vector lattices and closed polyhedral cones correspond; indeed, the category of finitely generated projective vector lattices is equivalent to the dual of a category whose objects are Euclidean closed polyhedral cones and whose morphisms consist of all piecewise homogeneous linear maps between such cones.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 2 , 01 April 1977 , pp. 243 - 254
Copyright
Copyright © Canadian Mathematical Society 1977

References

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