Least Integer Closed Groups
An a-closure of a lattice-ordered group is an extension which is maximal with respect to preserving the lattice of convex l-subgroups under contraction. We describe the a-closures of some local singular archimedean lattice-ordered groups with designated weak unit. In particular, we provide explicit descriptions of all of the a-closures of groups that are singularly convex, such as the group C(X, ℤ) of continuous integer-valued functions on a zero-dimensional space.
KeywordsVector Lattice Singular Part Riesz Space Prime Subgroup Weak Unit
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