6.35 (1978)

(R. Bieri, R. Strebel). Let $\mathfrak{o}$ be an associative ring with identity distinct from zero. A group $G$ is said to be almost finitely presented over $\mathfrak{o}$ if it has a presentation $G = F/R$ where $F$ is a finitely generated free group and the $\mathfrak{o}G$-module $R/[R, R]\otimes_{\mathbb{Z}} \mathfrak{o}$ is finitely generated. It is easy to see that every finitely presented group $G$ is almost finitely presented over $\mathbb{Z}$ and therefore also over an arbitrary ring $\mathfrak{o}$. Is the converse true?