On the embedding of a commutative ring in a local ring

R. Gilmer, W. Heinzer

Abstract. Let R be a commutative ring with identity. In this paper we consider conditions in order that there exists an embedding of R in a local ring. This leads naturally to an examination of conditions in order that a quasilocal ring (R,m) be dominated by a local ring. This, in turn, leads to a study of extensions of the residue field of a quasilocal ring. We prove several results concerning domination of a quasilocal ring by a local ring including the result that a zero-dimensional quasilocal ring that is embeddable in a Noetherian ring is dominated by an Artinian local ring.