# Questions tagged [semirings]

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### A semifield of characteristic zero may have a finite number of elements

A commutative semiring $(S, +, \cdot, 0, 1)$ with unity is said to be a semifield if for all $a, b\in S$, $a+b=0$ implies that $a=0$ and $b=0$, and $a.b=0$ implies that either $a=0$ or, $b=0$. I ...
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### Linear algebra over non-commutative semirings

I'm reading up on linear algebra over semirings, and I'm wondering why people seem to stop short of showing an equivalence between linear transformations between free modules and matrices. It seems ...
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### commutative rigs and the Grothendieck Group

If I start with a commutative rig, and apply the Grothendieck Group construction to it, twice, once to the additive structure and once to the multiplicative structure, is the result well-known? Does ...
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### Semirings with subtractive primes

Let $S$ be a commutative semiring with identity such that each prime ideal of $S$ is subtractive. Does this imply all ideals of $S$ to be subtractive? By a commutative semiring with identity I mean ...
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