# Tag Info

A ring $R$ is a triple $(R,+,\cdot)$ where $R$ is a nonempty set such that $(R,+)$ forms an abelian group, $(R,\cdot)$ forms a semigroup, and the two operations are related by the distributive laws: $a\cdot(b+c)=a\cdot b+a\cdot c$ and $(b+c)\cdot a=b\cdot a+c\cdot a$.
The semigroup $(R,\cdot)$ is not always required to have an identity, but when it does, $R$ is called a ring with identity. For questions about rings which don't necessarily have a unit element, the tag should be used.
The operation $\cdot$ does not have to be commutative, but when it is, $R$ is called a commutative ring.