On exact category of (m, n)-ary hypermodules

Abstract

We introduce and study category of (m, n)-ary hypermodules as a generalization of the category of (m, n)-modules as well as the category of classical modules. Also, we study various kinds of morphisms. Especially, we characterize monomorphisms and epimorphisms in this category. We will proceed to study the fundamental relation on (m, n)-hypermodules, as an important tool in the study of algebraic hyperstructures and prove that this relation is really functorial, that is, we introduce the fundamental functor from the category of (m, n)-hypermodules to the category (m, n)-modules and prove that it preserves monomorphisms. Finally, we prove that the category of (m, n)-hypermodules is an exact category, and, hence, it generalizes the classical case.

Direct Limit of (m, n)-ary Hypermodules

“…R. Ameri in [1] introduced and studied the category of hypergroups and hypermodules. Recently, various kinds of categories of hyperstructures have been studied in numerous papers(for instance see [1,21,22,27,[32][33][34][35]). In this paper, we follow [21] and introduce and study direct limit in the category of (m, n)-hypermodules.…”

“…Recently, various kinds of categories of hyperstructures have been studied in numerous papers(for instance see [1,21,22,27,[32][33][34][35]). In this paper, we follow [21] and introduce and study direct limit in the category of (m, n)-hypermodules. This work is a generalization of the paper A. Asadi, R. Ameri, Direct Limit of Krasner (m, n)-Hyperrings [8], with more details of categorical properties related to direct limit.…”

Spectrum of Zariski Topology in Multiplication Krasner Hypermodules

“…Hypergroup theory, which was defined in [1] as a more comprehensive algebraic structure of group theory, has been investigated by different authors in modern algebra. It has been developed using hyperring and hypermodule theory studies by many authors in a series of papers [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Following these papers, let us start by giving the basic information necessary for the algebraic structure that we will study as Krasner S-hypermodule in studying the S-hypermodule class on a fixed Krasner hyperring class S. Let N be a nonempty set; (N, •) is called a hypergroupoid if for the map defined as • : N × N −→ P * (N) is a function.…”