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.


Also see