The Importance and the Implications of the Study of Multiplicators On MTL-Algebra

The concept of maximal lattice of quotients for a distributive lattice was defined by J. Schmidt taking as a guide – line the construction of complete ring of quotients by partial morphisms introduced by G. Findlay and J. Lambeck. The central role in this construction is played by the concept of multiplier. The scope of this paper is to define the notion of multiplicators on MTLalgebra. There are also defined the notions of MTL-algebra of fractions and maximal MTL-algebra of quotients for a MTLalgebra. The results obtained in this paper for MTL-algebras are very analogous to ones obtained for BL-algebras. The main difference is that the equation x ? (x? y) ? x ? y is not valid for MTL-algebras. For this reason I have introduced a new axiom to define the notion of multiplicator.