On modules over groups
For a finite group G, by the endomorphism ring of a module M over a commutative ring R, we define a structure for M to make it an RG-module so that we study the relations between the properties of R-modules and RG-modules. Mainly, we prove that RadRM is an RG-submodule of M if M is an RG- module; also RadRM ? RadRGM where RadAM is the intersection of the maximal A-submodule of module M over a ring A. We also verify that M is an injective (projective) R-module if and only if M is an injective (projective) RG-module.
1979 ◽
Vol 28
(3)
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pp. 335-345
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1965 ◽
Vol 25
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pp. 113-120
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1997 ◽
Vol 122
(1)
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pp. 55-71
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1966 ◽
Vol 27
(2)
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pp. 721-731
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2020 ◽
Vol 9
(10)
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pp. 8869-8881
1993 ◽
Vol 42
(3)
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pp. 362-368