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In the first part of this monograph, we introduce the concept of join of baric algebras with an idempotent of weight 1 and the related concept of indecomposable (baric) algebra. A theorem of existence and unicity of decompositions for some baric algebras (those satisfying a.C.C. And d.C.C. Conditions) is obtained. Some well known examples in genetics are analyzed concerning decomposability and some questions are stated in this subject. In the second part, we obtain a peirce decomposition for some train algebras of rank n and, when n=4, some additional results are stated