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- Fully *-prime rings with involutionPublication . Mendes, D. I. C.Some known results on fully prime rings and almost fully prime rings are extended to the category of rings with involution. In particular, various properties of fully *-prime involution rings are presented, a classification of fully *-prime involution rings which satisfy a polynomial identity is given, and almost fully *-prime involution rings are characterized. The structure of the additive groups of these involution rings is also studied.
- On polynomial equation rings and radicalsPublication . Mendes, D. I. C.; Ochirbat, B.; Tumurbat, 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.