An ordered ring is a ring $R$ with a partial order such that for all elements $a,b,c$ in $R$, $a \leq b$ implies $a + c \leq b + c$, and $0 \leq a$ and $0 \leq b$ implies $0 \leq a \cdot b$.
Due to the reflexivity of the partial order, ordered rings may have zero divisors. Also, the trivial ring is an ordered ring.
Wikipedia, Partially ordered ring
Wikipedia, Ordered ring
Last revised on June 18, 2021 at 17:40:24. See the history of this page for a list of all contributions to it.