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

Ball, Richard N.

Canadian journal of mathematics, Tome 34 (1982) no. 3, pp. 621-661

Résumé

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].

Détail

DOI : 10.4153/CJM-1982-042-5

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