Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
권호 표지
DOI QR코드

DOI QR Code

The Prime Avoidance Lemma Revisited

  • Received : 2011.03.14
  • Accepted : 2011.11.18
  • Published : 2012.06.23
Download PDF
⟨ Previous Next ⟩

Abstract

We show that the above lemma and its well-known refinement are valid, in a general setting, in non-commutative rings. Some interesting consequences are also observed.

Keywords

References

  1. M. Alkan and Y. Tiras, Projective modules and prime submodules, Czechoslovak Math. J., 56(2)(2006), 601-611. https://doi.org/10.1007/s10587-006-0041-5
  2. F. Callialp and U. Tekir, On Finite Union of Prime Submodules, Pakistan Journal of Applied Sciences, 2(11)(2002), 1016-1017. https://doi.org/10.3923/jas.2002.1016.1017
  3. C. P. Lu, Unions of prime submodules, Houston J. Math, 23(2)(1997), 203-213.
  4. C. Faith, Rings and Things and a Fine Array of Twentieth Century Associative Algebra, Second Edition, American Mathematical Society, 2004.
  5. I. Kaplansky, Commutative Rings, Allyn and Bacon, Boston, MA, Revised Edition, The University of Chicago Press, 1970.
  6. O. A. S. Karamzadeh, Noetherian dimension, Ph. D. Thesis, Exeter, 1974.
  7. O. A. S. Karamzadeh, On the classical Krull dimension of rings, Fund Math, 117(1983), 103-108. https://doi.org/10.4064/fm-117-2-103-108
  8. O. A. S. Karamzadeh and B. Moslemi, On G-Type Domains, J. Algebra and its Applications, 5(2)(2012), 1-18.
  9. S. McAdam, Finite covering by ideals, Proceeding of the Oklahoma Conference (ring theory), Marcel-Dekker, INC. New York, 1974, 163-170.
  10. M. R. Pournaki and M. Tousi, A note on the countable union of prime submodules, Int. J. Math. Math. Sci., 27(2001), 641-643. https://doi.org/10.1155/S0161171201011085
  11. R. Y. Sharp, Steps in Commutative Algebra, Cambridge University Press, Second Edition, 2000.
  12. L. H. Rowen, Ring Theory, Vol I, Academic Press, New York, 1988.
  13. R. Y. Sharp, and P. Vamos, Baire's category theorem and prime avoidance in complete local rings, Arch. Math., 44(1985), 243-248. https://doi.org/10.1007/BF01237858

Cited by

  1. The Space of Maximal Subrings of a Commutative Ring vol.43, pp.2, 2015, https://doi.org/10.1080/00927872.2013.849264