Definition:Trivial Ring

Definition

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

• Trivial Ring is Commutative Ring

Sources

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {IV}$: Rings and Fields: $21$. Rings and Integral Domains: Example $21.5$