JOURNAL BROWSE
Search
Advanced SearchSearch Tips
The Prime Avoidance Lemma Revisited
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Kyungpook mathematical journal
  • Volume 52, Issue 2,  2012, pp.149-153
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2012.52.2.149
 Title & Authors
The Prime Avoidance Lemma Revisited
Karamzadeh, Omid Ali Shahny;
  PDF(new window)
 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
prime ideal;prime avoidance lemma;reducible;
 Language
English
 Cited by
1.
The Space of Maximal Subrings of a Commutative Ring, Communications in Algebra, 2015, 43, 2, 795  crossref(new windwow)
 References
1.
M. Alkan and Y. Tiras, Projective modules and prime submodules, Czechoslovak Math. J., 56(2)(2006), 601-611. crossref(new window)

2.
F. Callialp and U. Tekir, On Finite Union of Prime Submodules, Pakistan Journal of Applied Sciences, 2(11)(2002), 1016-1017. crossref(new window)

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.

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. crossref(new window)

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. crossref(new window)