On Prime Rings with Ascending Chain Condition on Annihilator Right Ideals and Nonzero Infective Right Ideals
1971 ◽
Vol 14
(3)
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pp. 443-444
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Keyword(s):
If I is a right ideal of a ring R, I is said to be an annihilator right ideal provided that there is a subset S in R such thatI is said to be injective if it is injective as a submodule of the right regular R-module RR. The purpose of this note is to prove that a prime ring R (not necessarily with 1) which satisfies the ascending chain condition on annihilator right ideals is a simple ring with descending chain condition on one sided ideals if R contains a nonzero right ideal which is injective.
2012 ◽
Vol 49
(3)
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pp. 366-389
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2020 ◽
Vol 57
(3)
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pp. 290-297
Keyword(s):
1965 ◽
Vol 8
(1)
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pp. 29-32
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Keyword(s):
1979 ◽
Vol 31
(3)
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pp. 558-564
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1961 ◽
Vol 101
(3)
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pp. 555
1972 ◽
Vol 13
(4)
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pp. 433-446
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