F-ring

In abstract algebra, a partially ordered ring is a ring (A, +, · ), together with a compatible partial order, i.e. a partial order ${\displaystyle \leq }$ on the underlying set A that is compatible with the ring operations in the sense that it satisfies:

and

for all ${\displaystyle x,y,z\in A}$. Various extensions of this definition exist that constrain the ring, the partial order, or both. For example, an Archimedean partially ordered ring is a partially ordered ring ${\displaystyle (A,\leq )}$ where ${\displaystyle A}$'s partially ordered additive group is Archimedean.

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