Abstract
The study of subsemimodules of semimodules over semirings plays a central role in the structure theory and are useful for many purposes. In this paper, [Formula: see text] is considered as an inverse semimodule over a semiring [Formula: see text] such that [Formula: see text] is a distributive lattice of rings. The main part of this paper is devoted to stating and proving several properties of vn-regular semimodules, which generalize the study of vn-regular modules.
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