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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 $ E$-uniserial if its lattice of fully invariant subgroups is totally ordered. Finite rank torsion-free reduced $ E$-uniserial groups are characterized. Such a group is a free module over the center $ C$ of its endomorphism ring, and $ C$ 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: $ E$-uniserial, torsion-free abelian group, valuation domain
Article copyright: © Copyright 1985 American Mathematical Society

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