Tag Archives: krull dimension

Dimension zero rings for three types of dimension

posted by on Wednesday September 20, 2017 with No comments! and filed under homological-algebra, model-theory | Tags: , ,

There are all sorts of notions of dimension that can be applied to rings. Whatever notion you use though, the ones with dimension zero are usually fairly simple compared with the rings of higher dimension. Here we'll look at three types of dimension and state what the rings of zero dimension look like with respect […]

Krull vs Global Dimension in Commutative Noetherian Rings

posted by on Wednesday June 17, 2015 with No comments! and filed under commutative-algebra, homological-algebra | Tags: ,

Let $R$ be a ring. The projective dimension $\mathrm{pd}_R(M)$ of an $R$-module $M$ is the infimum over the lengths of projective resolutions of $M$. The left global dimension of $R$ is the supremum over the projective dimensions of all left $R$-modules. There is a notion of right global dimension where left modules are replaced with […]