# A question of Rentschler and the Dixmier Problem

### Abstract

The following theorem is the main result of the paper.

THEOREM. Let $R$ and $T$ be somewhat commutative algebras with the same holonomic number and let $\varphi \colon R\to T$ be an algebra homomorphism. Then every holonomic $T$-module $M$ is (via $\varphi$) a holonomic $R$-module and has finite length as an $R$-module.