ON SMALL INJECTIVE RINGS AND MODULES
2009 ◽
Vol 08
(03)
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pp. 379-387
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A right R-module MR is called small injective if every homomorphism from a small right ideal to MR can be extended to an R-homomorphism from RR to MR. A ring R is called right small injective, if the right R-module RR is small injective. We prove that R is semiprimitive if and only if every simple right (or left) R-module is small injective. Further we show that the Jacobson radical J of a ring R is a noetherian right R-module if and only if, for every small injective module ER, E(ℕ) is small injective.
2008 ◽
Vol 2008
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pp. 1-6
1995 ◽
Vol 37
(3)
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pp. 373-378
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2017 ◽
Vol 21
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pp. 239-247
2009 ◽
Vol 80
(3)
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pp. 462-471
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1977 ◽
Vol 18
(1)
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pp. 101-104
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2006 ◽
Vol 2006
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pp. 1-13
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1969 ◽
Vol 21
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pp. 1404-1408
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1979 ◽
Vol 3
(1)
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pp. 31-35
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