Construction of some algebras of logic by using fuzzy ideals in mv-modules

We study the lattice structure of fuzzy A-ideals in an mv-module M (fai (M), symbolically) and show that it is a complete Heyting lattice and so the set of its pseudocomplements forms a Boolean algebra. In the sequel, the properties of fuzzy congruences in an mv-module are investigated and using them some structural theorems are stated and proved. Finally, it is proved that fai (M) can be embedded into the lattice of fuzzy congruences.