Fuzzy subsets on the non-empty set is a mapping of this set to the interval . The concept of fuzzy subgroups introduced from advanced concept of fuzzy set in group theory. In concept of fuzzy set there is the concept of relations is fuzzy relations. In this study examined that fuzzy relations related to the equivalence and congruence on a fuzzy group and fuzzy factor group. The results of this study was to show that a fuzzy relation if and if is a fuzzy congruence relations on fuzzy group and a fuzzy relation defined of is a fuzzy congruence relations on fuzzy factor group.
Abstract. Let R, S be rings with unity, M a module over S, where S a commutative ring, and f : R → S a ring homomorphism. A ring representation of R on M via f is a ring homomorphism µ : R → End S (M ), where End S (M ) is a ring of all S-module homomorphisms on M . One of the important properties in representation of ring is the Schur's Lemma. The main result of this paper is partly the generalization of Schur's Lemma in representations of ring on modules over a commutative ring 2010 Mathematics Subject Classifications: 16G10, 16W20, 12E15
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