Selections of lattice-ordered Groups |
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Authors: | Michael R Darnel |
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Institution: | (1) Department of Mathematical Sciences, Indiana University South Bend, South Bend, USA |
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Abstract: | It is well known that the quasitorsion class of archimedean -groups is the class of -groups G such that every closed convex -subgroup is a polar, and it is also well known that the class of -groups G such that every convex -subgroup is a polar is a torsion class. By defining a selection on -groups, these two results are generalized to show, whenever and are selections on -groups, the class of -groups G such that is a radical class. Three selections in particular — all convex -subgroups, all polars, and all closed convex -subgroups — and the radical classes determined by them are studied in some detail.
Received March 7, 2006; accepted in final form August 29, 2006. |
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Keywords: | 2000 Mathematics Subject Classification:" target="_blank">2000 Mathematics Subject Classification: Primary 06F15 secondary 06D22 20F60 |
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