When is every module with essential socle a direct sum of automorphism-invariant modules?
2019 ◽
Vol 19
(10)
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pp. 2050185
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The purpose of this paper is to study the structure of rings over which every essential extension of a direct sum of a family of simple modules is a direct sum of automorphism-invariant modules. We show that if [Formula: see text] is a right quotient finite dimensional (q.f.d.) ring satisfying this property, then [Formula: see text] is right Noetherian. Also, we show a von Neumann regular (semiregular) ring [Formula: see text] with this property is Noetherian. Moreover, we prove that a commutative ring with this property is an Artinian principal ideal ring.
2003 ◽
Vol 2003
(69)
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pp. 4373-4387
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2016 ◽
Vol 15
(09)
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pp. 1650160
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2019 ◽
Vol 18
(02)
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pp. 1950023
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Keyword(s):
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2019 ◽
Vol 19
(11)
◽
pp. 2050202
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1991 ◽
Vol 34
(3)
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pp. 364-367
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Keyword(s):
1999 ◽
Vol 60
(1)
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pp. 137-151
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