The Remak-Krull-Schmidt Theorem on\ Fuzzy Groups
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Abstract:
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.
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Journal title
volume 10 issue 6
pages 153- 159
publication date 2013-12-26
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