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The Generalized Orthocompletion and Strongly Projectable Hull of a Lattice Ordered Group

Published online by Cambridge University Press:  20 November 2018

Richard N. Ball
Richard N. Ball*
Affiliation:
Boise State University, Boise, Idaho
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The central result is the existence and uniqueness for an arbitrary l-group G of two hulls, Ḡ and Ḡω, which in the representable case coincide with the orthocompletion and strongly protectable hull of G. This is done by introducing two notions of extension, written ≼ and ≼ω, and proving that each G has a maximal ≼ extension Ḡ and a maximal ≼ω extension Ḡω. Two constructions of Ḡ and Ḡω are-given: an l-permutation construction leads to descriptive structural information, and a construction by “consistent maps” leads to a strong universal mapping property.

The notion of a strongly projectable hull has a lengthy history. The concept of an orthocompletion, together with the first proof of its existence and uniqueness, is due to Bernau [4]. Conrad summarized and extended all these results in an important paper [10].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 34 , Issue 3 , 01 June 1982 , pp. 621 - 661
Copyright
Copyright © Canadian Mathematical Society 1982

References

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