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Let R be a commutative ring. An R-module M is called a ω-Noetherian module if every submodule of M is of ω-finite type. R is called a ω-Noetherian ring if R as an R-module is a ω-Noetherian module.
In this paper, we present an exact version of the Eakin-Nagata Theorem on ω-Noetherian rings. To do this, we prove the Formanek Theorem for ω-Noetherian rings. Further, we point out by an example that the condition (†) in the Chung-Ha-Kim version of the Eakin-Nagata Theorem on SM domains is essential.
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참고문헌 (15)
참고문헌 신청
D. D. Anderson / 2000 / Two star operations and their induced lattices / Comm. Algebra 29 (5) : 2461 ~ 2475
E. Formanek / 1977 / Die st¨atze von Bertini f¨ur lokale Ringe / Math. Ann 229 : 97 ~ 111
F. G. Wang / 1997 / On w-modules over strong Mori domains / Comm. Algebra 25 (4) : 1285 ~ 1306
F. G. Wang / 1999 / On strong Mori domains / J. Pure Appl. Algebra 135 (2) : 155 ~ 165
F. G. Wang / 2010 / Finitely presented type modules and w-coherent rings / J. Sichuan Normal Univ 33 : 1 ~ 9
E. Formanek / 1977 / Die st¨atze von Bertini f¨ur lokale Ringe / Math. Ann 229 : 97 ~ 111
F. G. Wang / 1997 / On w-modules over strong Mori domains / Comm. Algebra 25 (4) : 1285 ~ 1306
F. G. Wang / 1999 / On strong Mori domains / J. Pure Appl. Algebra 135 (2) : 155 ~ 165
F. G. Wang / 2010 / Finitely presented type modules and w-coherent rings / J. Sichuan Normal Univ 33 : 1 ~ 9
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