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

Autor: Najmeh Jafarzadeh, Reza Ameri
Jazyk: angličtina
Rok vydání: 2020
Předmět:
Zdroj: Categories and General Algebraic Structures with Applications, Vol 12, Iss 1, Pp 69-88 (2020)
Druh dokumentu: article
ISSN: 2345-5853
2345-5861
Popis: 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.
Databáze: Directory of Open Access Journals