Free Magmas

This article introduces the free magmaM(X) constructed on a set X [6]. Then, we formalize some theorems aboutM(X): if f is a function from the set X to a magma N , the free magmaM(X) has a unique extension of f to a morphism ofM(X) into N and every magma is isomorphic to a magma generated by a set X under a set of relators on M(X). In doing it, the article defines the stable subset under the law of composition of a magma, the submagma, the equivalence relation compatible with the law of composition and the equivalence kernel of a function. We also introduce some schemes on recursive function.