Definition:Trivial Gradation

Definition
Let $\left({R, +, \circ}\right)$ be a ring.

Let $\left({M, \cdot, e}\right)$ be a monoid.

Define a grading on $R$ as follows:
 * $\displaystyle R_e = R$
 * $\displaystyle \forall m \in M \backslash \left\{{e}\right\} : R_m = \mathbf 0$

where $\mathbf 0$ is the zero ring.

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

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

Also see

 * Trivial Grading is Grading