@MISC{ALGSTR_4.MIZ,
  AUTHOR = {Riccardi, Marco},
  TITLE = {Free Magmas},
  SECTION1 = {Preliminaries},
  SECTION2 = {Equivalence Relations and Relators},
  SECTION3 = {Submagmas and Stable Subsets},
  SECTION4 = {Free Magmas},
  DAY = {20},
  MONTH = {October},
  YEAR = {2009},
  ADDRESS1 = {Casella Postale 49\\54038 Montignoso\\Italy},
  SUMMARY = {This article introduces the free magma $M(X)$ constructed on a set $X$ \cite{BourbakiAlgI}.
  Then, we formalize some theorems about $M(X)$: if $f$ is a function from the set $X$ to a
  magma $N$, the free magma $M(X)$ has a unique extension of $f$ to a morphism of $M(X)$ 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.}}

@BOOK{BourbakiAlgI,
       AUTHOR = {Nicolas Bourbaki},
        TITLE = {Elements of Mathematics. Algebra I. Chapters 1-3},
    PUBLISHER = {Springer-Verlag},
         YEAR = {1989},
      ADDRESS = {Berlin Heidelberg New York London Paris Tokyo}}
