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Abelian Groups Which are Uniserial as Modules over Their Endomorphism Rings

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1006)

Abstract

In a recent paper [4] S. Feigelstock considers (not necessarily associative) rings the ideal lattices of which are totally ordered. He calls such rings TOLI rings. Clearly, if Ris a TOLI ring, the lattice of fully invariant subgroups of its additive group R+ must be totally ordered, too. In this note we consider abelian groups A which possess this latter property.

Keywords

  • Abelian Group
  • Additive Group
  • Endomorphism Ring
  • Finite Rank
  • Ideal Lattice

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This research was supported in part by a University of Houston Research Enabling Grant

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References

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© 1983 Springer-Verlag Berlin Heidelberg

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Hausen, J. (1983). Abelian Groups Which are Uniserial as Modules over Their Endomorphism Rings. In: Göbel, R., Lady, L., Mader, A. (eds) Abelian Group Theory. Lecture Notes in Mathematics, vol 1006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21560-9_8

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  • DOI: https://doi.org/10.1007/978-3-662-21560-9_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12335-4

  • Online ISBN: 978-3-662-21560-9

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