2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/215562In this paper we extend the eliminant construction of Burchnall and Chaundy for commuting differential operators in the Heisenberg algebra to the q-deformed Heisenberg algebra and show that it again provides annihilating curves for commuting elements, provided q satisfies a natural condition. As a side result we obtain estimates on the dimensions of the eigenspaces of elements of this algebra in its faithful module of Laurent series.18 pages, 2 figures, LaTeX. Final version with some improvements in presentation. To appear in Journal of Algebra.Rings and AlgebrasQuantum Algebra16S99 (Primary) 81S05, 39A13 (Secondary)text