If V 1 is linearly closed and V 2 is linearly closed, then V 1 V 2 is linearly closed. Let us consider R and let us consider V . If x W , then x V . If v W , then - v W . If u W and v W , then u - v W .
V is a submodule of V .
Let X , V be strict right modules over R . Let us consider R , V . One can check that there exists a submodule of V which is strict. Suppose that for every vector v of V holds v W 1 iff v W 2 . Let V be a strict right module over R and W be a strict submodule of V .