Polars and their applications in directed interpolation groups

Glass, A. M. W.

doi:10.1090/S0002-9947-1972-0295991-3

Polars and their applications in directed interpolation groups
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Trans. Amer. Math. Soc. 166 (1972), 1-25 Request permission

Abstract:

In the study of l-groups, as in many other branches of mathematics, use is made of the concept of “orthogonal elements". The purpose of this paper is to show that this concept can be extended to directed, interpolation groups and that most of the theorems in l-groups concerning polars hold in the more general setting of directed, interpolation groups. As consequences, generalisations of Holland’s and Lorenzen’s theorems are obtained and a result on o-simple abelian, directed, interpolation groups.

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