Various Kinds of Freeness in the Categories of Krasner Hypermodules
The purpose of this paper is to study the concept of freeness in the categories of Krasner hypermodules over a Krasner hyperring. In this regards first we construct various kinds of categories of hypermodules based on various kinds of homomorphisms of hypermodules, such as homomorphisms, good homomorphisms, multivalued homomorphisms and etc. Then we investigate the notion of free hypermodule in these categories. This leads us to introduce different types of free, week free, ∗-free and fundamental free hypermodules and obtain the relationship among them.