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Orientador(es)
Resumo(s)
The notion of n-polynomial equation ring, for an arbitrary but fixed positive integer n, is introduced. A ring A is called an n- polynomial equation ring if γ(A[Xn]) = γ(A)[ Xn], for all radicals γ. If this equation holds for all hereditary radicals γ, then A is said to be a hereditary n-polynomial equation ring. Various characterizations of these rings are provided. It is shown that, for any ring A, the zero-ring on the additive group of A is an n- polynomial equation ring and that any Baer radical ring is a hereditary n- polynomial equation ring. New radicals based on these notions are introduced, one of which is a special radical with a polynomially extensible semisimple class.
Descrição
Palavras-chave
Amitsur rings Hereditary Amitsur rings Radicals Radicals with the Amitsur property
Contexto Educativo
Citação
Editora
Taylor & Francis