Module theory MOC

Module homomorphism

Let be a ring and be (left) -modules. A map is a (left) -module homomorphism or (left) -linear iff for any and module

This is a direct generalization of a linear map between vector spaces.

Properties

• A linear map is epic iff it is surjective iff
• A linear map is monic iff it is injective iff
• A linear map is an isomorphism iff it is bijective iff it is epic and monic
• If is a commutative ring, then is an -algebra called the Endomorphism ring.

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