On some properties of⊕-supplemented modules
2003 ◽
Vol 2003
(69)
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pp. 4373-4387
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Keyword(s):
A moduleMis⊕-supplemented if every submodule ofMhas a supplement which is a direct summand ofM. In this paper, we show that a quotient of a⊕-supplemented module is not in general⊕-supplemented. We prove that over a commutative ringR, every finitely generated⊕-supplementedR-moduleMhaving dual Goldie dimension less than or equal to three is a direct sum of local modules. It is also shown that a ringRis semisimple if and only if the class of⊕-supplementedR-modules coincides with the class of injectiveR-modules. The structure of⊕-supplemented modules over a commutative principal ideal ring is completely determined.
2019 ◽
Vol 19
(10)
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pp. 2050185
Keyword(s):
2016 ◽
Vol 15
(09)
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pp. 1650160
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Keyword(s):
2019 ◽
Vol 18
(02)
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pp. 1950023
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Keyword(s):
Keyword(s):
1980 ◽
Vol 23
(4)
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pp. 457-459
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Keyword(s):
Keyword(s):
1991 ◽
Vol 34
(3)
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pp. 364-367
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Keyword(s):
Keyword(s):