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The Remak-Krull-Schmidt Theorem on\\ Fuzzy Groups | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 13، دوره 10، شماره 6، اسفند 2013، صفحه 153-159 اصل مقاله (266.37 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2013.1337 | ||
| نویسندگان | ||
Babington Makamba1؛ Venkat Murali  2
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| 1Department of Mathematics, University of Fort Hare, Alice 5700 , Eastern Cape , South Africa | ||
| 2Department of Mathematics ( Pure & Applied ), Rhodes University, Grahamstown 6140, Eastern Cape, South Africa | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Preferential equality؛ Fuzzy subgroup؛ Direct product؛ Indecomposable؛ Isomorphism؛ Lattice | ||
| مراجع | ||
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