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Torsion Abelian RAI-Groups

Abstract

A subgroup A of an Abelian group G is called its absolute ideal if A is an ideal of any ring on G. An Abelian group is called an RAI-group if there exists a ring on it in which every ideal is absolute. The problem of describing RAI-groups was formulated by L. Fuchs (Problem 93). In this paper, absolute ideals of torsion Abelian groups and torsion Abelian RAI-groups are described.

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Correspondence to Pham Thi Thu Thuy.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 17, No. 8, pp. 109–138, 2011/12.

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Thuy, P.T.T. Torsion Abelian RAI-Groups. J Math Sci 197, 658–678 (2014). https://doi.org/10.1007/s10958-014-1749-7

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Keywords

  • Abelian Group
  • Direct Summand
  • Inductive Assumption
  • Quotient Ring
  • Torsion Group