Abstract :
This is a sequel to my previous papers on generalized power series. For the convenience of the reader I gather in the first section the definitions and results which shall be required. Any missing proof is either very easy or is already in one of the above quoted papers. After the preliminaries, I characterize (under suitable conditions) the generalized pow er series which are powers: the essential idea is to extend the validity of the usual binomial series. A short section gives conditions for a ring of generalized pou er series to be a real ring. As known the ring of usual power series with coefficients in a field, in any number of indeterminates, is a unique factorization domain. I show that the result holds for generalized power series with exponents in a free-ordered monoid which is noetherian and narrow. This leads to interesting examples of unique factorization domains. Completely integrally closed domains of generalized power series are also characterized in terms of their ring of coefficients and monoid of exponents. The final section is devoted to seminormal domains. The main results about usual power series are extended to generalized power series.
