The Ascending Chain Condition for Principal Ideals of Rings of Generalized Power Series.

Let (S, ≤) be a strictly totally ordered monoid and R a domain. It is shown in this paper that [[RS,≤]], the ring of generalized power series with coefficients in R and exponents in S. satisfies the ascending chain condition for principal ideals if and only if the ring R and the monoid S satisfy the ascending chain condition for principal ideals of R, and of S, respectively. [ABSTRACT FROM AUTHOR]