Cohen–Macaulayness from the first Buchsbaum–Rim coefficient
Let (R,m)({\bf R},{\mathfrak m})(R,m) be a Noetherian local ring with dimR≥2\dim {\bf R}\geq 2dimR≥2, and let U⊆mRrU\subseteq {\mathfrak m}{\bf R}^rU⊆mRr be a parameter module of Rr{\bf R}^rRr, where r>0r>0r>0. H…