Finite rank torsion-free abelian groups uniserial over their endomorphism rings

Author:
Jutta Hausen

Journal:
Proc. Amer. Math. Soc. **93** (1985), 227-231

MSC:
Primary 20K15

DOI:
https://doi.org/10.1090/S0002-9939-1985-0770526-1

MathSciNet review:
770526

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Abstract: An abelian group is -uniserial if its lattice of fully invariant subgroups is totally ordered. Finite rank torsion-free reduced -uniserial groups are characterized. Such a group is a free module over the center of its endomorphism ring, and is a strongly indecomposable discrete valuation ring. Properties similar to those of strongly homogeneous groups are derived.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1985-0770526-1

Keywords:
-uniserial,
torsion-free abelian group,
valuation domain

Article copyright:
© Copyright 1985
American Mathematical Society