A characterization of semilocal inertial coefficient rings

Abstract

A commutative ring R R with identity is called an inertial coefficient ring if every finitely generated R R -algebra A A with A / N A/N separable over R R contains a separable subalgebra S S such that S + N = A S + N = A , where N N is the Jacobson radical of A A . Thus inertial coefficient rings are those commutative rings R R for which a generalization of the Wedderburn Principal Theorem holds for suitable R R -algebras. Our purpose is to prove that a commutative ring with only finitely many maximal ideals is an inertial coefficient ring (if and) only if it is a finite direct sum of Hensel rings.