Von Neumann regular semimodule II

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.