ON CERTAIN NEW RADICALS ARISING FROM A GIVEN RADICAL

Abstract

If R is a ring and n is an integer weMaydefine a ring T_n (R) on the same underlying additive abelian group by using the formula a * b = nab to define a new multiplication. T_n , is a functor on the category of associative rings. If C is a class of rings then, for each n, the class C_n , is defined to consist of all rings R such that T_n (R) is in C. If C is a radical class then each class C_n , is also a radical class. We consider the properties of the radical class C which are inherited by C_n , and relationships between these classes C _n as n varies.