A magma is called equidecomposable when the operation is injective, or, in other words, if \(x+y=x'+y'\) implies that \(x=x'\) and \(y=y'\). A magma is free iff it is equidecomposable and graded, hence the notion of equidecomposability is very related to the notion of freeness although it is not sufficient. We study main properties of such magmas. In particular, an alternative characterization of freeness, which uses a weaker condition, is proved. We show how equidecomposable magmas can be split into two disjoint submagmas, one of which is free. Certain transformations on finite presentations permit to obtain a reduced form which allows us identify all the finite presented equidecomposable magmas up to isomorphisms.

当操作是内射时，或者如果\（x + y = x'+ y'\）暗示\（x = x'\）和\（y = y'\），则将岩浆称为等分解。。岩浆是自由的，前提是它是可分解和分级的，因此，尽管不充分，但是可分解性的概念与自由的概念非常相关。我们研究了这类岩浆的主要性质。特别是，证明了使用较弱条件的自由度的替代特征。我们展示了如何将可分解岩浆拆分成两个不相交的子岩浆，其中一个是免费的。有限表示的某些变换允许获得简化形式，这使我们能够识别所有同构同构的有限表示的可分解岩浆。