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Some Results on Locally Noetherian Modules and Locally Artinian Modules
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We prove that if R is a commutative ring, then every maximal ideal of R isidempotent if and only if every locally noetherian (locally artinian) R-module is semisim-ple.
Abstract
We prove that if R is a commutative ring, then every maximal ideal of R isidempotent if and only if every locally noetherian (locally artinian) R-module is semisim-ple.
참고문헌 (10)
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- I. S. Cohen, "Commutative rings with restricted minimum condition", Ducke Math. J., 17, pp.27~42 (1950)
- D. V. Huynh, "A characterization of locally Artinian modules", J. Algebra, 132, pp.287~293 (1990)
- T. Y. Lam, "Lectures on modules and rings" (1999), Springer-Verlag
- D. W. Sharp, "Vamos, Injective modules" (1971), Cambridge University Press
- H. H. Storrer, "On Goldman's primary decomposition", Lecture Notes in Math, 246, pp.617~661 (1972)
- A. Tuganbaev, "Rings close to regular" (2002), Kluwer Academic Publishers
- R. Wisbauer, "Foundations of module and ring theory" (1991), Gordon and Breach Science Publishers
관련 논문AI추천
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