Kasch Modules and pV-Rings
Keyword(s):
Let R be a ring. A right R-module M is called p-injective if every homomorphism from a principal right ideal of R to M can be given by a left multiplication. A ring R is called a right pV-ring if every simple R-module is p-injective. In this paper, Kasch modules are considered. It is proved that if a Kasch module M is finitely generated and quasi-p-injective, then there is a bijective correspondence between the class of maximal submodules of M and the class of all minimal left ideals of its endomorphism ring. Also, it is proved that if M is a pV-module which is a finitely generated projective self-generator, then its endomorphism ring is a right pV-ring. Finally, it is proved that being a right or left pV-ring is a Morita invariant.
2011 ◽
Vol 84
(3)
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pp. 433-440
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1997 ◽
Vol 63
(2)
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pp. 165-207
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1966 ◽
Vol 27
(2)
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pp. 697-708
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1988 ◽
Vol 31
(3)
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pp. 374-379
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2014 ◽
Vol 13
(08)
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pp. 1450060
1984 ◽
Vol 36
(2)
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pp. 193-205
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2009 ◽
Vol 146
(1)
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pp. 83-94
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2019 ◽
Vol 19
(11)
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pp. 2050207
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2004 ◽
Vol 2004
(30)
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pp. 1581-1588