The semirings tag has no usage guidance.

**-1**

votes

**1**answer

204 views

### An extension of the real semiring with multiple degrees of infinity

Is it possible to define an extension of the probability semiring $(\mathbb{R}^+, +, \times, 0, 1)$ such that
Closure $a^* = 1 + a + a^2 + \ldots$ is defined for every element of the semiring, not ...

**25**

votes

**0**answers

1k views

### Mikhalkin's tropical schemes versus Durov's tropical schemes

In Mikhalkin's unfinished draft book on tropical geometry, (available here) (page 26) he defines a notion of tropical schemes. It seems to me that this definition is not just a wholesale adaptation of ...

**18**

votes

**0**answers

610 views

### Categorification of the integers

I would like to know a natural categorification of the rig of integers $\mathbb{Z}$. This should be a $2$-rig. Among the various notions of 2-rigs, we obviously have to exclude those where $+$ is a ...

**5**

votes

**0**answers

110 views

### moduli in real/semi algebraic geometry

Is there a moduli space in semialgebraic geometry analogous to the Hilbert scheme in algebraic geometry?
The sort of thing I am imagining is an object in a category of semischemes:
Ordinary schemes ...

**3**

votes

**0**answers

132 views

### Semirings where solving linear systems is in P

Solving linear systems appears hard in semirings.
In $\mathbb{N}_0 (+,\times)$ it is NP-complete via reduction to 1-in-3 SAT.
In the min-plus semiring the complexity is $ NP \cap coNP$ according to ...

**2**

votes

**0**answers

104 views

### Quotients of the initial semiring

The natural numbers are the initial commutative semiring. Thus, for any commutative semiring $R$, there is a unique semiring map $\mathbb{N}\to R$.
For which $R$ is this map an epimorphism?
Some ...

**1**

vote

**0**answers

126 views

### Substitution semiring?

Let G be a [ CF ] grammar, and let elements of semiring be sets of rules.
Define multiplication as:
$$ x\otimes y = \{ t| \exists r \in x \exists s \in y (t=subst(r,s))\} $$
where $subst(r,s)$ ...