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- W2092425179 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." @default.
- W2092425179 created "2016-06-24" @default.
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- W2092425179 date "2014-01-09" @default.
- W2092425179 modified "2023-09-27" @default.
- W2092425179 title "A NOTE ON NIL AND JACOBSON RADICALS IN GRADED RINGS" @default.
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- W2092425179 doi "https://doi.org/10.1142/s0219498813501211" @default.
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