\documentclass[12pt]{article}
\usepackage{amsmath,amssymb,amsfonts}
\begin{document}
Let $R$ be a commutative Noetherian local ring. We show that $R$ is Gorenstein if and only if every finitely generated $R$-module can be embedded in a finitely generated $R$-module of finite projective dimension. This extends a result of Auslander and Bridger to rings of higher Krull dimension, and also improves a result due to Foxby where the ring is assumed to be Cohen-Macaulay.
\end{document}