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

• Definition:N-Graded Ring
• Definition:Z-Graded Ring

• Results about graded rings can be found here.

Sources

• 2002: Serge Lang: Algebra (Revised 3rd ed.): Chapter $\text {XVI}$: $\S 6$: Tensor product of algebras