Abstract
This chapter focuses on an isomorphism method for the study of I0n. By I0n is denoted a set of n-variate probability laws that have no indecomposable factor. By using a new method based on isomorphisms between some semigroups of probability laws is given a complete characterization of finite products of n-variate Poisson laws belonging to I0n. The theory of decompositions of probability laws has its origin in the well-known result conjectured by Levy and proved by Cramer in 1936, which states that any factor of a normal law is a normal law. The most important problem of this theory, stated by Raikov in 1938, is the problem of the characterization of the class of all the n-variate infinitely divisible laws having no indecomposable factor, which is identical with the class of all the n-variate probability laws having only infinitely divisible factors.
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