A NOTE ON RADICALS OF ASSOCIATIVE RINGS AND ALTERNATIVE RINGS

摘要

Let U be a universal subclass of a universal class V of rings. We investigate connections between radicals in U and V. We define T and T-s as follows: T = {A is an element of A(ss) every prime homomorphic image of A is not a hereditary Amitsur ring} T-s = {A is an element of A(ss) every prime homomorphic image of A has no nonzero ideal which is a hereditary Amitsur ring}. Let gamma is an element of {T,T-s} and let A be a commutative ring with minimum condition on ideals. We give a sufficient and necessary condition for A to be gamma-semisimple.