For any monoid $M$, we can naturally construct a semiring $S$ as follows: Let the additive monoid of $S$ be the free commutative monoid on $M$ Let the multiplicative monoid of $S …

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 …

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 resul …

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 wi …

q-product is defined as $x \otimes _q y = (x^{1-q}+y^{1-q}-1)^{1/(1-q)}$ Observation: $(+,\otimes_\infty)$ is min-plus tropical semiring on the segment $[0,1]$ $(+,\otimes_1)$ …

By an idempotent semiring I mean a set equipped with a join-semilattice with bottom structure $(0,+)$ and a multiplicative monoid $(1,\cdot)$ such that the following equations hold …

Hi everybody, let $f: [n] \times [n] \rightarrow \mathbb R_+$ be a nonnegative function and suppose that $f = \sum_{i = 1}^m f_i$ where the $f_i: [n] \times [n] \rightarrow \mathb …

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 who …

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