Takasi Nagahara

CLASSIFICATION OF RINGS SATISFYING SOME HERSTEIN'S CONDITION ON THE SET OF ALL NON-NILPOTENTS

Abstract Let be a non-commutative ring with center and let be the set of all nilpotents of . The following result is proved: If for every , there exists an integer , depending on , such that , then is one of five types whose structures can be determined abstractly.

INFINITE OUTER GALOIS THEORY OF SEMISIMPLE RINGS

Let B/A be an infinite outer Galois extension of semisimple rings and locally finite. Then, it is shown that there exites a 1 - 1 dual correspondense between intermediate rings of B/A and fat and closed subgloups of Aut(B/A) (= AutA(B) ), in the usual sense of Galois theory.