On the embedding of a commutative ring in a local ring

Abstract

Let $R$ be a commutative ring with identity. 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 $(R,\mathbf{m})$ be dominated by a local ring. This, in turn, leads to a study of extensions of the residue field of a quasilocal ring.