Definition:Non-Trivial Ring

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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.