Ring
Set
| context | ⟨X,+⟩∈AbelianGroup(X) |
| definiendum | ⟨X,+,∗⟩∈it |
| for all | a,b,c∈X |
| postulate | (a∗b)∗c=a∗(b∗c) |
| postulate | a∗(b+c)=(a∗b)+(a∗c) |
| postulate | (b+c)∗a=(b∗a)+(c∗a) |
Discussion
One might call the commutative group operation “+” the addition and the other one “∗” the multiplication. In a unital ring, the latter has an identity too.
One generally calls X the ring, i.e. the set where the operations “+” and “∗” are defined on.
Reference
Subset of
Context
