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

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.

Key Words:

• ACCP
• Generalized power series

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.