ON GRADED SEMI-PRIME RINGS
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Let G be a group with identity e and let R be a G-graded ring . In this article, we study the concept of graded semi-prime rings and we give some results on this concept. For example, we prove that if R is graded semi-prime and I is a graded ideal of R, then the set of all left annihilators of I equals the set of all right annihilators of I. Also, we prove that certain subsets should lie in the center of the graded semi-prime ring R.
Abstract
Let G be a group with identity e and let R be a G-graded ring . In this article, we study the concept of graded semi-prime rings and we give some results on this concept. For example, we prove that if R is graded semi-prime and I is a graded ideal of R, then the set of all left annihilators of I equals the set of all right annihilators of I. Also, we prove that certain subsets should lie in the center of the graded semi-prime ring R.
참고문헌 (4)
- M. Cohen, "Group-graded rings, smash products, and group actions", Trans. Amer. Math. Soc., 282, pp.237~258 (1984)
- E. C. Dade, "Group graded rings and modules", Math. Z., 174, pp.241~262 (1980)
- C. Nastasescu, "Graded ring theory" (1982), North Holland
- M. Refai, "On graded primary ideals", Turkish Journal of Mathematics, 28, pp.217~229 (2004)