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 May 12, 2022 at 12:05:17. See the history of this page for a list of all contributions to it.