The structure of a lattice-ordered group as determined by its prime subgroups
Author:
Keith R. Pierce
Journal:
Proc. Amer. Math. Soc. 40 (1973), 407-412
MSC:
Primary 06A55
DOI:
https://doi.org/10.1090/S0002-9939-1973-0337719-0
MathSciNet review:
0337719
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Abstract | References | Similar Articles | Additional Information
Abstract: We characterize by structure theorems the classes of all lattice-ordered groups in which (a) every prime subgroup is principal, (b) every proper prime subgroup is principal, and (c) every minimal prime subgroup is principal. These classes are also characterized by the structure of the root system of regular subgroups.
- [1] Paul Conrad, Some structure theorems for lattice-ordered groups, Trans. Amer. Math. Soc. 99 (1961), 212–240. MR 0121405, https://doi.org/10.1090/S0002-9947-1961-0121405-2
- [2] -, Lattice-ordered groups, Tulane University Lecture Notes, 1970.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1973-0337719-0
Keywords:
Lattice-ordered groups,
prime subgroups of a lattice-ordered group,
lex-sums of ordered groups,
lattice-ordered groups with a finite basis
Article copyright:
© Copyright 1973
American Mathematical Society