2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/215500Let $F$ be an arbitrary field. The Golod-Shafarevich example of a finitely generated nil $F$-algebra which is infinite dimensional -- is revisited. Here we offer a rather elementary treatment of that example, in which induction replaces Hilbert series techniques. This note also contains a detailed exposition of the construction of that example.Rings and Algebras16S15The Golod Shafarevich counter-example without Hilbert seriestext