Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

SOME REMARKS ON CAMILLO-KRAUSE CONJECTURE

  • Received : 2017.02.19
  • Accepted : 2017.07.26
  • Published : 2018.01.31
Download PDF
⟨ Previous Next ⟩

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?

Keywords

References

  1. A. N. Alahmadi, PI-rings with Artinian proper cyclics are Noetherian, Int. Electron. J. Algebra 13 (2013), 40-42.
  2. A. Al-Huzali, S. K. Jain, and S. R. Lopez-Permouth, Rings whose cyclics have finite Goldie dimension, J. Algebra 153 (1992), no. 1, 37-40. https://doi.org/10.1016/0021-8693(92)90147-E
  3. M. Behboodi and S. Roointan-Isfahani, Almost uniserial rings and modules, J. Algebra 446 (2016), 176-187. https://doi.org/10.1016/j.jalgebra.2015.09.024
  4. V. Camillo and G. Krause, Problem 12, Rings, modules and representations, 133-137, Contemp. Math., 480, Amer. Math. Soc., Providence, RI, 2009.
  5. N. V. Dung, D. V. Huynh, P. F. Smith, and R. Wisbauer, Extending Modules, Pitman, London, 1994.
  6. N. Er, Some remarks on a question of Faith, Contemp. Math. 480 (2009), 133-137.
  7. C. Faith, Algebra II, Springer, Berlin, 1976.
  8. S. K. Jain, A. K. Srivastava, and A. A. Tuganbaev, Cyclic Modules and the Structure of Rings, Oxford Mathematical Monographs, Oxford University Press, 2012.
  9. T. Y. Lam, Lectures on Modules and Rings, Springer-Verlag, New York, 1999.
  10. J. C. McConnell and J. C. Robson, Noncommutative Noetherian Rings, Wiley-Interscience, New York, 1987.
  11. A. Shamsuddin, Rings with krull dimension one, Comm. Algebra 26 (1998), no. 7, 2147-2158. https://doi.org/10.1080/00927879808826266
  12. L. W. Small, Semihereditary rings, Bull. Amer. Math. Soc. 73 (1967), 656-658. https://doi.org/10.1090/S0002-9904-1967-11812-3
  13. C. Somsup, N. V. Sanh, and P. Dan, On serial Noetherian rings, Comm. Algebra 34 (2006), no. 10, 3701-3703. https://doi.org/10.1080/00927870600860858