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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Polars and their applications in directed interpolation groups

Author: A. M. W. Glass
Journal: Trans. Amer. Math. Soc. 166 (1972), 1-25
MSC: Primary 06A55
MathSciNet review: 0295991
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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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Keywords: Carrier, convex directed subgroup, directed, interpolation property, antilattice, polar, prime subgroup, prime filter, bipolar, representable directed, interpolation group
Article copyright: © Copyright 1972 American Mathematical Society