TY - JOUR
ID - 80792
TI - On exact category of $(m, n)$-ary hypermodules
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Jafarzadeh, Najmeh
AU - Ameri, Reza
AD - Department of Mathematics, Payamenoor University,P.O. Box 19395-3697, Tehran, Iran.
AD - Mathematics, School of Mathematics, Statistics and Computer
Science, University of Tehran
Y1 - 2020
PY - 2020
VL - 12
IS - 1
SP - 69
EP - 88
KW - $(m
KW - n)$-hypermodules
KW - kernel
KW - cokernel
KW - balanced category
KW - fundamental functor
KW - exact category
DO -
N2 - 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.
UR - http://cgasa.sbu.ac.ir/article_80792.html
L1 - http://cgasa.sbu.ac.ir/article_80792_907e526521584c03372aaada0e600e45.pdf
ER -