Definition:Trivial Gradation

Definition
Let $\struct {R, +, \circ}$ be a ring.

Let $\struct {M, \cdot, e}$ be a monoid.

Define a gradation on $R$ as follows:
 * $R_e = R$
 * $\forall m \in M \setminus \set e : R_m = \mathbf 0$

where $\mathbf 0$ is the zero ring.

This is called the trivial $M$-gradation on $R$.

Also known as
A trivial gradation is also known as a trivial grading.

Also see

 * Trivial Gradation is Gradation