On the atomic property for power series rings (Q1964153)

Let \(D\) be an integral domain. Then \(D\) is said to be atomic if each non-zero non-unit of \(D\) is a product of irreducible elements (i.e., atoms). If \(D[X]\) is atomic, then certainly \(D\) is atomic. However, the author [\textit{M. Roitman}, J. Pure Appl. Algebra 87, No. 2, 187-199 (1993; Zbl 0780.13014)] gave a construction of an atomic integrally closed domain \(D\) (in fact, every nonzero irreducible element of \(D\) is a product of two atoms) with \(D[X]\) not atomic. In this paper, he shows that \(D[[X]]\) is also not atomic. Conversely, he gives an example of a non-atomic domain \(D\) such that \(D[[X]]\) is atomic, in fact, any reducible element of \(D[[X]]\) with nonzero constant term is a product of two atoms.