The Remak-Krull-Schmidt Theorem on\\ Fuzzy Groups
نویسندگان
1 Department of Mathematics ( Pure & Applied ), Rhodes University, Grahamstown 6140, Eastern Cape, South Africa
2 Department of Mathematics, University of Fort Hare, Alice 5700 , Eastern Cape , South Africa
doi
10.22111/ijfs.2013.1337چکیده
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.
