# Questions tagged [semiring]

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### Difference Ternary and gamma

Difference between ternary semiring and gamma semiring. There are many articles found on both topics. But what is the major difference between ternary and gamma
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### Well-ordered commutative semirings

I am interested in the characterization of the most important types of numbers from an axiomatic viewpoint. For example, every complete ordered field is isomorphic to the field of real numbers. In ...
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### Is there a name for a ring with a distinguished absorbing element (for both addition and multiplication)?

There's a standard notion of a monoid with zero in algebra, which is a monoid $M$ having a distinguished element $0$ such that $0m=0=m0$ for all $m\in M$. Is there a common name for the ring analogue ...
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### Is there a closed form for the recursively defined function $f_{n+1}(x) := f_n(x)^{f_n(x)}$.

Is there a closed form$^*$ for the following recursive function: \begin{align} f_0(x) &:= x\\ f_{n+1}(x) &:= f_n(x)^{f_n(x)} \end{align} Assuming that $x$ is an element of a semi-ring$^\dagger$...
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### The spectrum of a semiring

One of the generalizations of algebraic geometry is provided by the theory of semiring schemes, viz. Lorscheid 2012. The theory follows the same set up of scheme theory, but we use semirings instead ...
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### Are affine semiring schemes equivalent to semirings?

One of the generalizations of algebraic geometry is provided by the theory of semiring schemes, cf. Lorscheid 2012. The theory follows the same set up of scheme theory, but we use semirings instead of ...
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### Identity elements of semirings

When we define a group the identity element can be any suitable one. E.g. $(\mathbb{N}, 0, +, -)$ or $(\mathbb{N}, 1, \cdot , N_i^{-1})$ are two groups with $2$ different identity elements. Now it is ...
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### Additive and multiplicative identities of a semiring can coincide.

Semiring $(S, \oplus, \otimes, \bar{0}, \bar{1})$ is an algebraic structure in which $(S, \oplus, \otimes)$ is a monoid and $(S, \otimes, \bar{1})$ is a semigroup and multiplication $\otimes$ ...
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### Semirings of small orders

A semiring is a structure $(R, +, 0, *)$ such that $(R, +, 0)$ is a commutative monoid, $(R, *, 0)$ is a semigroup with zero, and the distributive laws hold. I know that there were attempts at ...
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### Additive identity of a semiring and sub semiring.

We know that the identity of a group and its sub groups are same. But I think in case of semirings, the additive identity of a sub semiring may be distinct from that of the semiring. I see a counter ...
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1 vote
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### Can you help me with a semi-ring problem please?

The problem: Let $X = \mathbb{R}$ Define $S = \{ G \subseteq \mathbb{R} : G$ is at most countable $\}$ $\cup$ $\{\emptyset \}$. Show $S$ is a semi-ring. Here is what I have so far. Well the ...
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### Is every idempotent semiring a completely regular?

A semiring $(S, +, \cdot)$ is said to be a completely regular semiring if for every $a\in S$, there exists some $x\in S$ satisfying the following conditions: (1) $a=a+x+a$ (2) $a+x=x+a$ and (...
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Edit: In a semiring $(R, +, \cdot, 0, 1)$, $0$ and $1$ are additive identity and multiplicative identity, respectively such that $0$ is multiplicatively absorbing, that is $0\cdot a=0=a\cdot 0$ for ...
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Define the ideals of a semiring as follows: A non empty subset $I$ of a semiring $S$ is said to be a left (resp. right) ideal of $S$ if: (1) $a+b\in I$ for all $a, b\in I$ and (2) $sa$ (resp. $... 5 votes 2 answers 258 views ### Homomorphism of a set to its power set. Let$(S, +, \cdot, 0)$and$(S', \oplus, \otimes, 0')$be two semirings. Then$f: S\rightarrow S'$is said to be a homomorphism if for all$a, b\in S,f(a+b)=f(a)\oplus f(b)$,$f(a.b)=f(a)\otimes f(...
Let $(S, \oplus, \otimes)$ be a commutative semiring and $H$ be a subset of $S$ such that for all $x, y\in H$ implies that $x\otimes y= e$ where $e$ is the multiplicative identity( i.e., the ...