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Abstract
It was shown by Bergman that the Jacobson radical of a Z-graded ring is homogeneous. This paper shows that the analogous result holds for nil radicals, namely, that the nil radical of a Z-graded ring is homogeneous. It is obvious that a subring of a nil ring is nil, but generally a subring of a Jacobson radical ring need not be a Jacobson radical ring. In this paper, it is shown that every subring which is generated by homogeneous elements in a graded Jacobson radical ring is always a Jacobson radical ring. It is also observed that a ring whose all subrings are Jacobson radical rings is nil. Some new results on graded-nil rings are also obtained.
Original language | English |
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Article number | 1350121 |
Number of pages | 8 |
Journal | Journal of algebra and its applications |
Volume | 13 |
Issue number | 4 |
DOIs | |
Publication status | Published - Jun 2014 |
Keywords
- Graded rings
- nil rings
- nil radical
- Jacobson radical
- SEMIGROUP RINGS
Projects
- 1 Finished