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Locally Flat Vector Lattices

Published online by Cambridge University Press:  20 November 2018

Marlow Anderson
Marlow Anderson*
Affiliation:
Purdue University at Fort Wayne, Fort Wayne, Indiana
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Let G be a lattice-ordered group (l-group). If X ⊆ G, then let

Then X’ is a convex l-subgroup of G called a polar. The set P(G) of all polars of G is a complete Boolean algebra with ‘ as complementation and set-theoretic intersection as meet. An l-subgroup H of G is large in G (G is an essential extension of H) if each non-zero convex l-subgroup of G has non-trivial intersection with H. If these l-groups are archimedean, it is enough to require that each non-zero polar of G meets H. This implies that the Boolean algebras of polars of G and H are isomorphic. If K is a cardinal summand of G, then K is a polar, and we write G = K⊞K'.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 32 , Issue 4 , April 1980 , pp. 924 - 936
Copyright
Copyright © Canadian Mathematical Society 1980

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