On essential extensions of direct sums of either injective or projective modules
2014 ◽
Vol 13
(07)
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pp. 1450038
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Keyword(s):
For a ring R, there are classical facts that R is right Noetherian if and only if every direct sum of injective right R-modules is injective, and R is right Noetherian if and only if every essential extension of a direct sum of injective hulls of simple right R-modules is a direct sum of injective right R-modules. In this paper, we prove that R is right Noetherian if and only if every essential extension of a direct sum of injective hulls of simple right R-modules is a direct sum of either injective right R-modules or projective right R-modules.
2017 ◽
Vol 10
(03)
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pp. 1750049
Keyword(s):
1988 ◽
Vol 31
(2)
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pp. 243-247
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Keyword(s):
2017 ◽
Vol 60
(4)
◽
pp. 791-806
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Keyword(s):
1994 ◽
Vol 17
(4)
◽
pp. 661-666
Keyword(s):
1981 ◽
Vol 33
(4)
◽
pp. 817-825
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Keyword(s):
1990 ◽
Vol 33
(1)
◽
pp. 11-17
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Keyword(s):