The Remak-Krull-Schmidt Theorem on\\ Fuzzy Groups

Document Type : Research Paper

Authors

1 Department of Mathematics, University of Fort Hare, Alice 5700 , Eastern Cape , South Africa

2 Department of Mathematics ( Pure & Applied ), Rhodes University, Grahamstown 6140, Eastern Cape, South Africa

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.

Keywords

References

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