Three Theorems on Form Rings
Three Theorems on Form Rings
Three theorems concerning the form ring (= associated graded ring) ${\mathbf {F}}\left ( {R,I} \right )$ of an ideal $I$ in a Noetherian ring $R$ are proved. The first characterizes, for a $P$-primary ideal in a locally quasi-unmixed ring, when ${\mathbf {F}}{\left ( {R,I} \right )_{\operatorname {red}}}$ is an integral …