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Notes on Chain Rings and Radicals
Tumurbat, Sodnomkhorloo,Dayantsolmon, Dagva,Khulan, Tumenbayar Department of Mathematics 2018 Kyungpook mathematical journal Vol.58 No.3
We investigate connections in the classes of rings with chain property and the lattice of strongly hereditary radicals.
Baatar Ochirbat,Deolinda I. C. Mendes,Sodnomkhorloo Tumurbat 경북대학교 자연과학대학 수학과 2020 Kyungpook mathematical journal Vol.60 No.4
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.