Bernoullicity of lopsided principal algebraic actions (Q6594745)

\textit{D. J. Rudolph} and \textit{K. Schmidt} [Invent. Math. 120, No. 3, 455--488 (1995; Zbl 0835.28007)] showed Bernoullicity for algebraic \(\mathbb{Z}^d\)-actions by automorphisms of compact abelian groups with completely positive entropy. Essentially the same basic construction readily builds algebraic actions of other groups, and \textit{D. Lind} and \textit{K. Schmidt} [Ergodic Theory Dyn. Syst. 42, No. 9, 2923--2934 (2022; Zbl 1508.37015)] extended the Bernoullicity result to certain `principal algebraic actions' (equivalent to cyclic modules over the integral group ring of the acting group). Building on work of \textit{B. Hayes} [Compos. Math. 157, No. 10, 2160--2198 (2021; Zbl 1477.37015)] similar results are obtained here for certain finitely-generated modules under a `lopsidedness' condition under an orderability condition on the acting group.