Abstract:
In the paper, Malcev rings are defined. The class of Malcev rings strictly contains rings of Malcev–Neumann series, formal skew Laurent series rings, and formal pseudo-differential operator rings. In the paper, ring-theoretic properties of Malcev rings are studied. It turns out that rings of Malcev–Neumann series, formal skew Laurent series rings, and formal pseudo-differential operator rings have similar ring-theoretic properties related to the existence of the filtration with respect to the lowest degree of the series.
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