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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Invariants for a class of torsion-free abelian groups
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by D. Arnold and C. Vinsonhaler
Proc. Amer. Math. Soc. 105 (1989), 293-300
DOI: https://doi.org/10.1090/S0002-9939-1989-0935102-X

Abstract:

In this note we present a complete set of quasi-isomorphism invariants for strongly indecomposable abelian groups of the form $G = G({A_1}, \ldots ,{A_n})$. Here ${A_1}, \ldots ,{A_n}$ are subgroups of the rationals $Q$ and $G$ is the kernel of $f:{A_1} \oplus \cdots \oplus {A_n} \to Q$, where $f({a_1}, \ldots ,{a_n}) = \Sigma {a_i}$. The invariants are the collection of numbers ${\text {rank}} \cap \{ G[\sigma ]|\sigma \in M\}$, where $M$ ranges over all subsets of the type lattice generated by $\left \{ {{\text {type}}({A_i})} \right \}$. Our results generalize the classical result of Baer for finite rank completely decomposable groups, as well as a result of F. Richman on a subset of the groups of the form $G({A_1}, \ldots ,{A_n})$.
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Bibliographic Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 105 (1989), 293-300
  • MSC: Primary 20K15
  • DOI: https://doi.org/10.1090/S0002-9939-1989-0935102-X
  • MathSciNet review: 935102