Abstract
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.
This paper is dedicated to Paul Conrad on the occasion of his 80th birthday.
AMS Subject Classifications. 06F25, 20F60 Keywords, lattice-ordered groups, archimedean groups, singular groups, hyperarchimedean, rings of continuous functions, groups of continuous functions
This author was partially supported by a doctoral fellowship from the Florida Education Fund and was Van Vleck Visiting Assistant Professor of Mathematics at Wesleyan University during the development of this work. She thanks both institutions for their generosity.
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© 2002 Springer Science+Business Media Dordrecht
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Hager, A.W., Kimber, C.M., McGovern, W.W. (2002). Least Integer Closed Groups. In: Martínez, J. (eds) Ordered Algebraic Structures. Developments in Mathematics, vol 7. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3627-4_13
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DOI: https://doi.org/10.1007/978-1-4757-3627-4_13
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