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Some Classes of Hopfian Abelian Groups

Abstract

This paper describes the Hopfian groups in some classes of Abelian groups. A complete description of Hopfian divisible groups is presented; on the basis of this description, the study of Hopficity of arbitrary Abelian groups is reduced to the study of Hopficity of reduced groups. Direct sums of cyclic groups that are Hopfian groups are characterized. Finally, the paper looks at specific examples of rings whose additive groups are Hopfian.

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Correspondence to E. V. Kaygorodov.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 17, No. 8, pp. 59–61, 2011/12.

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Kaygorodov, E.V. Some Classes of Hopfian Abelian Groups. J Math Sci 197, 623–624 (2014). https://doi.org/10.1007/s10958-014-1744-z

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Keywords

  • Abelian Group
  • Cyclic Group
  • Additive Group
  • Commutative Ring
  • Algebraic System