Modules Whose Cyclic Submodules Have Finite Dimension
1976 ◽
Vol 19
(1)
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pp. 1-6
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Keyword(s):
R denotes an associative ring with identity. Module means unitary right R-module. A module has finite Goldie dimension over R if it does not contain an infinite direct sum of nonzero submodules [6]. We say R has finite (right) dimension if it has finite dimension as a right R-module. We denote the fact that M has finite dimension by dim (M)<∞.A nonzero submodule N of a module M is large in M if N has nontrivial intersection with nonzero submodules of M [7]. In this case M is called an essential extension of N. N⊆′M will denote N is essential (large) in M. If N has no proper essential extension in M, then N is closed in M. An injective essential extension of M, denoted I(M), is called the injective hull of M.
1971 ◽
Vol 23
(2)
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pp. 345-354
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2004 ◽
Vol 70
(1)
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pp. 163-175
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2017 ◽
Vol 10
(03)
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pp. 1750049
Keyword(s):
1989 ◽
Vol 40
(1)
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pp. 109-111
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Keyword(s):
1968 ◽
Vol 11
(1)
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pp. 19-21
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Keyword(s):
1994 ◽
Vol 17
(4)
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pp. 661-666
Keyword(s):
1988 ◽
Vol 44
(2)
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pp. 242-251
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Keyword(s):
1972 ◽
Vol 24
(2)
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pp. 209-220
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1980 ◽
Vol 23
(2)
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pp. 173-178
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Keyword(s):
2012 ◽
Vol 54
(3)
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pp. 605-617
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