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Torsion Abelian afi-Groups

Abstract

This paper is devoted to the study of Abelian afi-groups. A subgroup A of an Abelian group G is called its absolute ideal if A is an ideal of any ring on G. We will call an Abelian group an afi-group if all of its absolute ideals are fully invariant subgroups. In this paper, we will describe afi-groups in the class of fully transitive torsion groups (in particular, separable torsion groups) and divisible torsion groups.

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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. 139–145, 2011/12.

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Thuy, P.T.T. Torsion Abelian afi-Groups. J Math Sci 197, 679–683 (2014). https://doi.org/10.1007/s10958-014-1750-1

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Keywords

  • Abelian Group
  • Prime Number
  • Cyclic Group
  • Torsion Group
  • Invariant Subgroup