Definition:Trivial Ring

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A ring $\struct {R, +, \circ}$ is a trivial ring if and only if:

$\forall x, y \in R: x \circ y = 0_R$

Also defined as

Some sources refer to a trivial ring as what is defined on $\mathsf{Pr} \infty \mathsf{fWiki}$ as a null ring: a ring with one element.

Also see