On Prime Ideals Related to an Ideal in a Commutative Ring

This article focuses on the notion of prime ideal related to an ideal of a commutative ring. Some of its characteristics are studied and the relations between ideals and prime ideals related to these ideals in a commutative ring are examined. Then some useful connections among them are obtained. Both similarities and differences between prime ideals related to an ideal and prime ideals are pointed out. Moreover a direct connection between prime ideals related to an ideal and radical ideals is obtained.

Keywords:

Prime Ideal, Radical Ideal Localization,

PDF

___

Anderson, D. D., & Bataineh, M. (2008). Generalizations of prime ideals. Communications in Algebra, 36, 686-696.
Anderson, D. D., & Smith, E. (2003). Weakly prime ideals. Houston Journal of Mathematics, 29, 831-840.
Atiyah, M. F., & MacDonald, I. G. (1969). Introduction to Commutative Algebra. Addison-Wesley.
Ebrahimpour, M., & Nekooei, R. (2012). On generalizations of prime ideals. Communications in Algebra, 40, 1268-1279.
Jenkins, J., & Smith, P.F. (1992). On the prime radical of a module over a commutative ring. Communications in Algebra, 20, 3593-3602.
Kaplansky, I. (1974). Commutative Rings. The University of Chicago.
Kirby, D. (1966). Components of ideals in a commutative ring. Ann. Mat. Pura Appl., 4, 109-125.
Kirby, D. (1969). Closure operations on ideals and submodules. J. London. Math. Soc., 44, 283-291.
Lam, T. Y. (2001). A First Course in Noncommutative rings. Springer.
Lam, T. Y., & Reyes, M. L. (2008). A prime ideal principle in commutative algebra. Journal of Algebra, 319, 3006-3027.
Matsumura, H. (1986). Commutative Ring Theory. Cambridge University Press.
McConnell, J. C., & Robson, J. C. (1987). Noncommutative Noetherian Rings. Wiley Chichester.
Naghipour, A. R. (2005). A simple proof of Cohen’s theorem. The American Mathematical Monthly, 112, 825-826.
Öneş, O. (2019). A generalization of prime ideals in a commutative ring. In: Proceedings Book of the 2nd Mediterranean International Conference of Pure Applied Mathematics and Related Areas, Paris, France, 28-31 August, 124-126.
Öneş, O. (2020). On radical formula in modules over noncommutative rings. Filomat, 34(2), 443-449.
Öneş, O., & Alkan, M. (2017). On the left O-prime ideals over a noncommutative ring. Advanced Studies in Contemporary Mathematics, 27(1), 107-113.
Öneş, O., & Alkan, M. (2018). A note on graded ring with prime spectrum. Advanced Studies in Contemporary Mathematics, 28(4), 625-634.
Öneş, O., & Alkan, M. (2019a). Multiplication modules with prime spectrum. Turkish Journal of Mathematics, 43(4), 2000-2009.
Öneş, O., & Alkan, M. (2019b). Zariski subspace topologies on ideals. Hacettepe Journal of Mathematics and Statistics, 48(6), 1667-1674.

Gazi University Journal of Science Part A: Engineering and Innovation-Cover

Yayın Aralığı: Yılda 4 Sayı
Başlangıç: 2013
Yayıncı: Gazi Üniversitesi, Fen Bilimleri Enstitüsü

Arşiv