Tag Archives: local ring

A Case of No Positive Finite Projective Dimension

A commutative Noetherian local ring $ R$ with maximal ideal $ M$ is called a regular local ring if the Krull dimension of $ R$ is the same as the dimension of $ M/M^2$ as a $ R/M$-vector space. In studying regular local rings one often uses the following lemma in inductive arguments: if $ […]