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


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