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http://dx.doi.org/10.5666/KMJ.2020.60.4.711

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)
Publication Information
Kyungpook Mathematical Journal / v.60, no.4, 2020 , pp. 711-721 More about this Journal
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
Amitsur rings; hereditary Amitsur rings; radicals; radicals with the Amitsur property;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
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