Factorization in Hurwitz series domain (Q660466)

Let \(A\) be a commutative ring with identity and \(HA\) the set of formal expressions of the type \(f=\sum_{i=0}^{\infty} a_i X^i\) where \(a_i\in A\). Then \(HA\) is a commutative ring with identity with respect to the following operations: for every \(f=\sum_{i=0}^{\infty} a_i X^i, g=\sum_{i=0}^{\infty} b_i X^i\in HA\), \(f+g=\sum_{i=0}^{\infty} (a_i+b_i) X^i\), and \(f\ast g=\sum_{n=0}^{\infty} c_n X^n\) where \(c_n=\sum_{i=0}^{n} C_n^i a_i b_{n-i}\) and \(C_n^i=\frac{n!}{i!(n-i)!}\). The author discusses factorization in \(HA\) and in its subring of Hurwitz polynomials.