Module theory MOC

Annihilator

Let be a (left) -module and . The annihilator is the (left) ideal made up of all elements of which annihilate , module i.e.

If is a submodule, then is a two-sided ideal.

Proof of ideal

If then for any we have

so . With the additional assumption that is a submodule, we have

so as required.

See also

• Faithful module

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