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Abelian dqt-Groups and Rings on Them

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Abstract

The absolute radical of an Abelian group G is the intersection of radicals of all associative rings with additive group G. The problem of describing absolute radicals was formulated by L. Fuchs. He described the absolute Jacobson radical of a torsion Abelian group. In this work, the absolute Jacobson radical and the absolute nil-radical are investigated in some mixed Abelian group classes.

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Correspondence to E. I. Kompantseva.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 3, pp. 53–67, 2013.

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Kompantseva, E.I. Abelian dqt-Groups and Rings on Them. J Math Sci 206, 494–504 (2015). https://doi.org/10.1007/s10958-015-2328-2

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Keywords

  • Abelian Group
  • Associative Ring
  • Invariant Subgroup
  • Pure Subgroup
  • Basic Subgroup