Definition:Trivial Gradation
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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.