# Tag Archives: dimension

## On a characterisation of Krull dimension zero rings

Here is one characterisation of commutative rings of Krull dimension zero: Theorem. A commutative ring $R$ has Krull dimension zero if and only if every element of the Jacobson radical ${\rm Jac}(R)$ of $R$ is nilpotent and the quotient ring $R/{\rm Jac}(R)$ is von Neumann regular. Recall that a ring $R$ is von Neumann regular […]