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Ordinary algebra of formal power series in one variable is convenient tostudy by means of the algebra of Riordan matrices and the Riordan group. Inthis paper we consider algebra of formal power series without constant term,isomorphic to the algebra of formal Dirichlet series. To study it, we introducematrices, similar to the Riordan matrices. As a result, some analogies betweentwo algebras becomes visible. For example, the Bell polynomials (polynomials ofpartitions of number $n$ into $m$ parts) play a certain role in the ordinaryalgebra. Similar polynomials (polynomials of decompositions of number $n$ into$m$ factors) play a similar role in the considered algebra. Analog of theLagrange series for the considered algebra is also exists. In connection withthis analogy, we introduce matrix group, similar to the Riordan group andcalled the Riordan-Dirichlet group. As an example, we consider analog of theAbel's identities for this group.

Algebra of formal power series, isomorphic to the algebra of formal Dirichlet series