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essential submodule
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(Definition)
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Let $X$ be a submodule of a module $Y$ . We say that $X$ is an essential submodule of $Y$ , and that $Y$ is an essential extension of $X$ , if whenever $A$ is a nonzero submodule of $Y$ , then $A \cap X$ is also nonzero.
A monomorphism $f : X \to Y$ is an essential monomorphism if the image ${\rm im} f$ is an essential submodule of $Y$ .
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"essential submodule" is owned by antizeus.
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Cross-references: image, monomorphism, module, submodule
There are 6 references to this entry.
This is version 2 of essential submodule, born on 2002-01-05, modified 2003-09-20.
Object id is 1374, canonical name is EssentialSubmodule.
Accessed 6014 times total.
Classification:
| AMS MSC: | 16D80 (Associative rings and algebras :: Modules, bimodules and ideals :: Other classes of modules and ideals) |
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Pending Errata and Addenda
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