On subsemimodules of semimodules

P. J. Allen [1] introduced the notion of a $Q$-ideal and a construction process was presented by which one can build the quotient structure of a semiring modulo a $Q$-ideal. Here we introduce the notion of $Q_M$-subsemimodule $N$ of a semimodule $M$ over a semiring $R$ and construct the factor semimodule $M/N$. It is shown that this notion inherits most of the essential properties of the factor modules over a ring.