Multiplication $(m,n)$-hypermodules

The concept of multiplication $(m,n)$-hypermodules was introduced by Ameri and Norouzi in \cite{sorc2}. Here we intend to investigate extensively the multiplication $(m,n)$-hypermodules. Let $(M,f,g)$ be a $(m,n)$-hypermodule (with canonical $(m,n)$-hypergroups) over a commutative Krasner $(m,n)$-hyperring $(R,h,k)$. A $(m, n)$-hypermodule $(M, f, g)$ over $(R, h, k)$ is called a multiplication $(m, n)$-hypermodule if for each subhypermodule $N$ of $M$, there exists a hyperideal $I$ of $R$ such that $N =g(I, 1^{(n-2)}, M)$.