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