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Types Of Homomorphisms Direct Image Fancy Definition Of Module Submodule

1	Types Of Homomorphisms
1	Direct Image
2	Fancy Definition Of Module
3	Submodule

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Essential Submodule

Let be a submodule of a module . We say that is an essential submodule of , and that is an essential extension of , if whenever is a nonzero submodule of , 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 .