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Some remarks on Camillo-Krause conjecture

Bahram Amirsardari
대한수학회 (The Korean Mathematical Society)|2018.01|대한수학회논문집 (Communications of the KMS)|제33권 제1호|pp. 45-51

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참고문헌

키워드

Noetherian moduleCamillo-Krause ringArtinian module
주제분류수학

초록

This paper contains some results that grew out of an attempt to Camillo-Krause conjecture: Is a ring $R$ right Noetherian if for each nonzero right ideal $I$ of $R$, $R/I$ is an Artinian right $R$-module?

Abstract

This paper contains some results that grew out of an attempt to Camillo-Krause conjecture: Is a ring $R$ right Noetherian if for each nonzero right ideal $I$ of $R$, $R/I$ is an Artinian right $R$-module?

참고문헌 (13)

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  3. M. Behboodi, "Almost uniserial rings and modules", J. Algebra, 446, pp.176~187 (2016)[DOI]
  4. V. Camillo, "Problem 12, Rings, modules and representations", Contemp. Math., 480, pp.133~137 (2009), Amer. Math. Soc.
  5. N. V. Dung, "Extending Modules" (1994), Pitman
  6. N. Er, "Some remarks on a question of Faith", Contemp. Math., 480, pp.133~137 (2009)
  7. C. Faith, "Algebra II" (1976), Springer
  8. S. K. Jain, "Cyclic Modules and the Structure of Rings, Oxford Mathematical Monographs" (2012), Oxford University Press
  9. T. Y. Lam, "Lectures on Modules and Rings" (1999), Springer-Verlag
  10. J. C. McConnell, "Noncommutative Noetherian Rings" (1987), Wiley-Interscience
  11. A. Shamsuddin, "Rings with krull dimension one", Comm. Algebra, 26(7), pp.2147~2158 (1998)[DOI]
  12. L. W. Small, "Semihereditary rings", Bull. Amer. Math. Soc., 73, pp.656~658 (1967)[DOI]
  13. C. Somsup, "On serial Noetherian rings", Comm. Algebra, 34(10), pp.3701~3703 (2006)[DOI]

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