A NOTE ON w-NOETHERIAN RINGS

作者：Xing Shiqi^*; Wang Fanggui

来源：Bulletin of the Korean Mathematical Society, 2015, 52(2): 541-548.

DOI：10.4134/BKMS.2015.52.2.541

• w-moudle
• w-finite type
• w-Noetherian module
• w-Noetherian ring

Let R be a commutative ring. An R-module M is called a w-Noetherian module if every submodule of M is of w-finite type. R is called a w-Noetherian ring if R as an R-module is a w-Noetherian module. In this paper, we present an exact version of the Eakin-Nagata Theorem on w-Noetherian rings. To do this, we prove the Formanek Theorem for w-Noetherian rings. Further, we point out by an example that the condition (dagger) in the Chung-Ha-Kim version of the Eakin-Nagata Theorem on SM domains is essential.

• 出版日期2015-3
• 单位四川师范大学