Definition:Non-Trivial Ring
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Definition
A non-trivial ring is a ring which is not trivial.
That is, a ring $R$ such that:
- $\exists x, y \in R: x \circ y \ne 0_R$
where $0_R$ denotes the zero of $R$.
Also known as
Some sources use a non-hyphenated version of the term: nontrivial ring.