On polynomial equation rings and radicals

Mendes, D. I. C.; Ochirbat, B.; Tumurbat, S.

http://hdl.handle.net/10400.6/9663

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Authors

Mendes, D. I. C.

Ochirbat, B.

Tumurbat, S.

Abstract(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.