Isomorphism Theorems in the Primary Categories of Krasner Hypermodules

Let R be a Krasner hyperring. In this paper, we prove a factorization theorem in the category of Krasner R-hypermodules with inclusion single-valued R-homomorphisms as its morphisms. Then, we prove various isomorphism theorems for a smaller category, i.e., the category of Krasner R-hypermodules with strong single-valued R-homomorphisms as its morphisms. In addition, we show that the latter category is balanced. Finally, we prove that for every strong single-valued R-homomorphism and , we have Ker(f)+a=a+Ker(f)={xA is an element of vertical bar f(x)=f(a)}.