Assertion: ring | /r/HasProperty | abelian group
Facets:
value: under addition
type: OTHER
value: under a monoid under multiplication
type: OTHER
value: with a second binary operation
type: OTHER
Source sentences:
text: A ring is an abelian group with a second binary operation that is associative, is distributive over the abelian group operation, and has an identity element (this last property is not required by some authors, see § Notes on the definition).
text: To form a ring these two operations have to satisfy a number of properties: the ring has to be an abelian group under addition as well as a monoid under multiplication, where multiplication distributes over addition; i.e., a ⋅ (b + c) = (a ⋅ b) + (a ⋅ c).