Algebraic and Diagonable Rings

Abstract

1. Introduction. In a well-known paper (7) Jacobson has shown how his structure theory for arbitrary rings can be applied to give more precise information about the so-called “algebraic” algebras. This specialization of his general theory is, however, perhaps not completely satisfying in that it deals only with algebras, i.e. rings admitting a field of operators, whereas neither the general structure theory nor the definition of the property of being “algebraic” seems to depend in any essential way on the precise nature of the operators.