Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On n-Amitsur Rings

  • Ochirbat, Baatar (Department of Mathematics, Mongolian University of Science and Technology) ;
  • Mendes, Deolinda I.C. (Department of Mathematics, University of Beira Interior) ;
  • Tumurbat, Sodnomkhorloo (Department of Mathematics, National University of Mongolia and School of Applied Science and Technology)
  • Received : 2019.08.25
  • Accepted : 2020.07.21
  • Published : 2020.12.31
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Abstract

The concepts of an Amitsur ring and a hereditary Amitsur ring, which were introduced and studied by S. Tumurbat in a recent paper, are generalized. For a positive integer n, a ring A is said to be an n-Amitsur ring if γ(A[Xn]) = (γ(A[Xn]) ∩ A)[Xn] for all radicals γ, where A[Xn] is the polynomial ring over A in n commuting indeterminates. If a ring A satisfies the above equation for all hereditary radicals γ, then A is said to be a hereditary n-Amitsur ring. Characterizations and examples of these rings are provided. Moreover, new radicals associated with n-Amitsur rings are introduced and studied. One of these is a special radical and its semisimple class is polynomially extensible.

Keywords

Acknowledgement

The first and third authors were partly supported by the Science and Technology Fund of Mongolia, Grant No. Shuss2017/64. The second author was partly supported by the research project: Grant UID/MAT/00212/2019 - financed by FEDER through the - Programa Operacional Factores de Competividade, FCT - Fundação para a Ciência e Teconologia.

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