I've found an algorithm that only seems to make sense in the case of ordered semirings such that $A > AB$ iff $A \neq 0$ and $B = 0$. Is there a name for (semirings with) such an ordering? The property holds for the natural numbers, but not for number sets having $0 \neq n < 1$.
Ordered semirings s.t. $A > AB$ iff $A \neq 0$ and $B = 0$
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abstract-algebra
order-theory
semiring