Almost Graded Prime Ideals

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.