The generalized Oppenheim expansions for the direct product of non-Archimedean fields

The well-known Oppenheim expansion algorithm in the field $\mathbb{Q}_p$ is generalized to the ring $\mathbb{Q}_g$, where $g=p_1\cdot\ldots\cdot p_{N}$. The metric properties of the digits of this expansion and also the metric properties of the coefficients of some expansions of polyadic numbers are studied.