ABSTRACT
A traditional method for studying the structure of module-finite associative algebras has been to separate the algebra into a separable subalgebra and a radical subalgebra. The purpose of this paper is to investigate conditions under which both the summand and the intersection properties of the Wedderburn Principal Theorem can be extended to more general base rings with the prime radical substituted for the Jacobson radical. The Wedderburn Principal Theorem, described anachronistically, states that a field is an inertial coefficient ring with the trivial intersection property. Brown refers to these extensions of the Wedderburn Principal Theorem as "satisfying a splitting property". The splitting property of the Wedderburn Principal Theorem relative to the prime radical may be studied from several different viewpoints. The chapter gives several classes of Noetherian and “almost” Noetherian rings which are f-split WIC-rings.
