Partial bases and homological stability of GL₍ (R) revisited

Let R be a unital ring satisfying the invariant basis number property, that every stably free R-module is free, and that the complex of partial bases of every finite rank free module is Cohen--Macaulay. This class of rings includes every ring of stable rank 1 (e. g. any local, semi-local or Artinian ring), every Euclidean domain, and every Dedekind domain OS of arithmetic type where |S| > 1 and S contains at least one non-complex place. Extending recent work of Galatius--Kupers--Randal-Williams and Kupers--Miller--Patzt, we prove that the sequence of general linear groups GLₙ (R) satisfies slope-1 homological stability with Z1/2-coefficients.