Module over a commutative unital ring
This article is about a basic definition in commutative algebra. View a complete list of basic definitions in commutative algebra
- is a monoid action of the multiplicative monoid of on , viz.:
- is an additive homomorphism from (treated as an additive group) to the additive group of all functions from to itself, under pointwise addition. In symbols:
It follows that and
- The map is an endomorphism of , viewed as an Abelian group.
All the above three conditions can be stated concisely as: the map homomorphism of unital rings , where .