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

Categories and General Algebraic Structures with Applications

Najmeh Jafarzadeh¹  Reza Ameri² 

[1] Department of Mathematics, Payamenoor University,P.O. Box 19395-3697, Tehran, Iran.;Mathematics, School of Mathematics, Statistics and Computer Science, University of Tehran;

关键词: $(m;    n)$-hypermodules;    kernel;    cokernel;    balanced category;    fundamental functor;    exact category;   

DOI  :  

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown