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<p>Various constructions of generalized Alexander quandles are studied.It is proved that, up&#xa0;to isomorphism, they reduce to two types.Conditions are found under which such quandles are abelian.A construction of an extension of a generalized Alexander quandle to the direct product of&#xa0;two groups is given.Conditions for constructing a quandle over a module and a near-ring are found.</p>

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Constructions of Quandles over Groups, Modules, and Near-Rings

  • 期刊论文

  • 发表日期：

    2026年1月29日

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  • A. N. Borodin,
  • M. V. Neshchadim,
  • A. A. Simonov

摘要

Various constructions of generalized Alexander quandles are studied.It is proved that, up to isomorphism, they reduce to two types.Conditions are found under which such quandles are abelian.A construction of an extension of a generalized Alexander quandle to the direct product of two groups is given.Conditions for constructing a quandle over a module and a near-ring are found.