Journal of Mathematics and Statistics

Almost Graded Prime Ideals

Ameer Jaber, Malik Bataineh and Hani Khashan

DOI : 10.3844/jmssp.2008.231.235

Journal of Mathematics and Statistics

Volume 4, Issue 4

Pages 231-235

Abstract

Problem Statement: Graded commutative ring with unity over an abelian group were introduced by many authors such as T. Y. Lam and C. T. C. Wall, and almost prime ideals over commutative rings with unity were introduced by S.M. Batwadeker and P.K. Sharma, and this forced us to try to extend the theory of almost and n-almost prime ideals to the graded case. Approach: We develop the theory of almost and n-almost prime ideals to the graded case. Results: We extended some basic results about almost and n-almost prime ideals to the graded case, and then we gave a relationship between n-almost graded prime ideals and weakly graded prime ideals. Conclusion: The extended results about almost and n-almost graded prime ideals allow us to classify further properties about almost graded prime ideals. 2000 AMS Mathematics Subject Classification: 13 A 02.

Copyright

© 2008 Ameer Jaber, Malik Bataineh and Hani Khashan. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.