Definition:Graded Ring

Definition
Let $M$ be a semigroup.

An $M$-graded ring is a pair $\struct {R, f}$ where:
 * $R$ is a ring
 * $f$ is a gradation of type $M$ on the additive group of $R$ which is compatible with the ring structure of $R$.

Also known as
An $M$-graded ring is also known as a graded ring of type $M$.

Also see

 * Definition:Graded Ring Homomorphism

Special cases

 * Definition:N-Graded Ring
 * Definition:Z-Graded Ring