This is a disjoint union over all possible binary partitions of A. It is straightforward to show that multiplication is associative and commutative (up to isomorphism), and distributive over addition. As for the generating series, (F · G)(x) = F(x)G(x).
This is a disjoint union over all possible binary partitions of A. It is straightforward to show that mul.tiplication is? associative and: com!m,utative (up to isomorphism), and distributive over addition. As for the generating se.ries (F · G)(x) = F(x)G(x)