Partial bases and homological stability of GLₕ(R) revisited

Let R R be a unital ring satisfying the invariant basis number property, that every stably free R 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 1 (e.g., any local, semi-local or Artinian ring), every Euclidean domain, and every Dedekind domain O S O_S of arithmetic type where | S | > 1 |S| > 1 and S S contains at least one noncomplex place. Extending recent work of Galatius–Kupers–Randal-Williams and Kupers–Miller–Patzt, we prove that the sequence of general linear groups GL n ⁡ ( R ) GL_n(R) satisfies slope- 1 1 homological stability with Z [ 1 / 2 ] Z[1/2] -coefficients.