Abstract
Let (S, ≤) be a strictly totally ordered monoid and R a domain. It is shown in this paper that [[R S,≤]], 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.
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Acknowledgment
The author wishes to express his sincere thanks to the referee for his/her valuable suggestions.
The author was supported by National Natural Science Foundation of China (10171082), TRAPOYT and NWNU-KJCXGC212.
Notes
#Communicated by B. Huisgen-Zimmermann.