Venkat Murali
Department of Mathematics ( Pure & Applied ), Rhodes University, Grahamstown 6140, Eastern Cape, South Africa
[ 1 ] - The Remak-Krull-Schmidt Theorem on\ Fuzzy Groups
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 som...
[ 2 ] - Fuzzy Subgroups of Rank Two Abelian p-Group
In this paper we enumerate fuzzy subgroups, up to a natural equivalence, of some finite abelian p-groups of rank two where p is any prime number. After obtaining the number of maximal chains of subgroups, we count fuzzy subgroups using inductive arguments. The number of such fuzzy subgroups forms a polynomial in p with pleasing combinatorial coefficients. By exploiting the order, we label the s...
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