1PG&Research Department of Mathematics, Jamal Mohamed college, Trichirappalli-20 E-mail:
2Department of Mathematics, J J College of Engineering & Technology, Trichirappalli-09 E-mail:
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A Technique of generating of Q-fuzzy R-sub module by a given arbitrary Qfuzzy set is provided. It is shown that (i) The sum of two Q-fuzzy R-sub module of a module M is the Q-fuzzy R-sub module generated by their union and (ii) The set of all Q-fuzzy sub module of a given module forms a complete lattice. Consequently it is established that the collection of all Qfuzzy R-sub module, having the same values at zero, of M of the lattice of Qfuzzy R-sub module of M. Interrelationship of these finite range sub lattices is established. Finally it is shown that the lattice of all Q-fuzzy R-sub module of M can be embedded into a lattice of Q-fuzzy R-sub module of M. Through out this paper, M denote as Q-fuzzy R-sub module where R is the commutative near ring with unity. Characterization of Q-fuzzy left R-sub modules with respect to t-norm are also given.
Q-fuzzy set, Q-fuzzy R-sub module, Level sub module, Q-fuzzy lattice of R-sub modules, Lattice homomorphism, Modular lattice
