Artinness of Generalized Macaulay–Northcott Modules

Abstract

Let R be an associated ring not necessarily with identity, M a left R-module having the property (F), and (S, ≤) a strictly totally ordered monoid which is also artinian and finitely generated. It is shown that the module [M ^S,≤] consisting of generalized inverse polynomials over M is an artinian left [[R ^S,≤]]-module if and only if M is an artinian left R-module.

Key Words:

• Artinian module
• Generalized Macaulay–Northcott module
• Ring of generalized power series

2000 Mathematics Subject Classification:

• 16W60
• 13E10

ACKNOWLEDGMENTS

The authors thank the referee for his/her useful comments and suggestions. This research supported by National Natural Science Foundation of China (10171082), Foundation for University Key Teacher by the Ministry of Education of China (GG-110-10736-1001) and by NWNU-KJCXGC-03-18.

Notes

Communicated by I. Swanson.