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 OS 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) GLₙ (R) satisfies slope- 1 1 homological stability with Z 1 / 2 Z1/2 -coefficients.
Bernard et al. (Tue,) studied this question.