TY - JOUR
ID - 1337
TI - The Remak-Krull-Schmidt Theorem on\ Fuzzy Groups
JO - Iranian Journal of Fuzzy Systems
JA - IJFS
LA - en
SN - 1735-0654
AU - Makamba, Babington
AU - Murali, Venkat
AD - Department of Mathematics, University of Fort Hare, Alice
5700 , Eastern Cape , South Africa
AD - Department of Mathematics ( Pure & Applied ), Rhodes University,
Grahamstown 6140, Eastern Cape, South Africa
Y1 - 2013
PY - 2013
VL - 10
IS - 6
SP - 153
EP - 159
KW - Preferential equality
KW - Fuzzy subgroup
KW - Direct product
KW - Indecomposable
KW - Isomorphism
KW - Lattice
DO - 10.22111/ijfs.2013.1337
N2 - In this paper we study a representation of a fuzzy subgroup $mu$ of a group $G$, as a product of indecomposable fuzzy subgroups called the components of $mu$. This representation is unique up to the number of components and their isomorphic copies. In the crisp group theory, this is a well-known Theorem attributed to Remak, Krull, and Schmidt. We consider the lattice of fuzzy subgroups and some of their properties to prove this theorem. We illustrate with some examples.
UR - https://ijfs.usb.ac.ir/article_1337.html
L1 - https://ijfs.usb.ac.ir/article_1337_e18fbd0fd51a1501715cd4e7c8fc4138.pdf
ER -