The semigroups tag has no wiki summary.

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### Proving that a semigroup is regular

In a number of diverse situations of interest to me (mostly associated with something called the abelian sandpile model), one can define a nonabelian semigroup generated by commuting elements ...

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### Automorphisms of $P(\Bbb N)$

I believe I've proved that the power semigroup of non-negative integers with addition has a trivial automorphism group. The proof is a bit long, completely elementary and rather unremarkable (as the ...

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### What can we say about a semigroup that's acted on by an ideal of polynomials?

This got no response on MSE, so posting here.
Let $S = \{ (a,b) \in \Bbb{Z}^2 : \gcd(a,b) \neq 1 \} \cup (1,1)$. Then $S$ forms a semigroup. The operation being componentwise multiplication.
Let ...

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### series representation for *un*bounded perturbations of semigroup generators

Let $A$ generate an analytic $C_0$-semigroup on a Banach space $X$ and $B$ be a relatively compact perturbation, i.e., $B$ is compact as an operator from $D(A)$ (with the graph norm) to $X$. Then ...

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### Progress on group languages characterizations

Def. A group language is a recognizable language whose syntactic monoid is a group.
q1. Is it known a "nice" combinatorial characterization of group languages ?
q1.1. If no, is it well understood ...

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### What is the probability two random maps on n symbols commute?

It is well known that two randomly chosen permutations of $n$ symbols commute with probability $p_n/n!$ where $p_n$ is the number of partitions of $n$. This is a special case of the fact that in a ...

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### Hindman's theorem variant for noncommutative semigroups

The well set proof of Hindman's finite sums theorem applied to noncommutative semigroups yields a sequence of elements such that finite products ordered coherently with this sequence are in one set. ...

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137 views

### Idempotents in Green J classes

I recently read this article Syntactic semigroups. In page $8$, he speaks about a J class having an idempotent is called regular:
A $\mathcal J$-class containing an idempotent is called regular. ...

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293 views

### Generalized free product of semigroups with amalgamated subsemigroups

Hanna Neumann in
[American Journal of Mathematics, 1948,
http://www.jstor.org/discover/10.2307/2372201?uid=2&uid=4&sid=21102497379451 ]
introduced a notion of generalized free product of ...

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201 views

### Strongly continuous semigroups that cannot be contractions

Let $X$ be a Banach space, and $(P_t)_{t \ge 0}$ a strongly continuous semigroup of bounded operators on $X$. Using the uniform boundedness principle, it's simple to prove that there are constants ...

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### Existence of a possible counterexample in automaton semigroups

In an attempt to resolve a question posed by Cain in his paper on Automaton Semigroups (open problem 6.12), I would like to know if there exists a finite semigroup $S$ satisfying the following ...

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60 views

### Is there a strongly stable semigroup which is not uniformly bounded

Let $X$ be a Hilbert space and let $(T(t))_{t\geq 0}$ a $C_0$-semigroup on $X$, we recall that:
1- $(T(t))_{t\geq 0}$ is said to be uniformly bounded if there exists $M\geq 0$ such that for all ...

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55 views

### Transformation terminology question

Given a transformation $t$ from the transformation semigroup $T_{n}$, if you take powers of $t$ under composition you get a length $s$ stem followed by a cycle. Permutations by definition have a ...

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232 views

### For a monoid with zero $M$, how many additive operations on $M$ can there be making $M$ a ring?

Let $(M,\times)$ be a monoid with zero. Let $\Sigma(M,\times)$ be the set of binary operations $+$ on $M$ such that $(M,+,\times)$ is a ring. Let $\sim$ be an equivalence relation on ...

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### How much do idempotent ultrafilters generate in terms of semigroups?

It is known that the set of ultrafilters on, say, the natural numbers $\mathbb{N}$, can naturally be endowed with the structure of a compact topological left semigroup (which fails to be anything ...

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### What are the semigroups in which congruence classes can be multplied like sets?

For a semigroup $S$ and a congruence $\rho$ on $S$, let's say that $\rho$ is good when for all $a,b\in S$ we have that $[ab]=[a][b],$ where $[x]$ denotes the congruence class of $x$ modulo $\rho$ and ...

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### Cauculation of a conplex integrand. A question from the book PDE by A. Friedman

In the book Partial Diferential Equations by A. Friedman 1969.
Part 2
on page 104, in the proof of theorem 2.1 (d).
A is a operator of type $(\psi,M)$ ($-A$generate a analytic semigroup), and ...

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179 views

### Embedding a semigroup into a divisible semigroup

The following is motivated by the fact that I'd like to have a way, much better if canonical, to isometrically embed a normed group into a normed divisible group. But semigroups are a much more ...

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261 views

### Projective limit construction of a semigroup

Let $\tilde{\mathbb N}$ be the Abelian semigroup (under addition) given by $\mathbb N\cup\{0,\infty\}$, and let $S_n$ be the Abelian monoid $\tilde{\mathbb N}^{2^n}$ under point-wise addition. ...

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### What is the way to after finding Cohen-Macaulay semigroup as ring of monomial?

http://people.missouristate.edu/lesreid/reu/2007/PPT/robin.ppt
it said missing part inside and not missing part outside is non Cohen-Macaulay semigroup
which determine whether is missing in the ...

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382 views

### On the notion of partial semigroup

A partial binary operation on a set $X$ is just a (partial) function $\varphi: X \times X \rightharpoonup X$ (I'm using \rightharpoonup for partial maps), and a partial magma is a pair $\mathbb M = ...

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### How many idempotent relations are there on an $n$-element set?

As far as I know, it is an open problem to give a formula counting transitive relations on an $n$-element set. Is it easier to count the idempotent relations, that is relations that are both ...

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### on the set of numbers generated by integer linear combination of two real numbers.

Let $b > a > 0$ be two real numbers. I am interested in the set of numbers
$X(p,q) = p a + q b$ with $p,q$ positive integers. Basically this is the set $a \mathbb{N} + b \mathbb{N}$.
What ...

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### On exponential formula

Let $T(t),t\geq 0$, be a $C_0$-semigroup on a Banach space $X$. If $A$ is the infinitesimal generator of $T(t),t\geq 0$, then
$$T(t)x=\lim_{n\infty}(I-\frac{t}{n}A)^{-n}x$$
for every $x \in X, t\geq ...

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### Continuity of multiplicative character

Let $G$ be a discrete group and $\beta (G)$ denote the Stone-Cech compactification of $G$, a right topological semigroup. By a multiplicative character, I mean a mapping that preserves multiplication ...

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### A question of terminology - Unitizations of semigroups

There are at least two standard ways of unitizing a (small) semigroup $\mathbb A$:
(i) We add an identity regardless that $\mathbb A$ is already unital.
(ii) We add an identity only if none is ...

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### Generator of a $C_0$-semigroup restricted to a subspace

Suppose we have a decreasing filtration of Banach spaces $(E_t)\_{t\geq0}$, inclusions $V_{s+t,t}:E_{s+t}\to E_t$ and projections $P_{t,s+t}:E_t\to E_{s+t}$ such that $P_{t,s+t}V_{s+t,t}=I_{E_{s+t}}$. ...

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### Semiflows and continuous symmetries

Given a differential equation on a Banach space $\mathcal{X}$ of the form $\frac{d u}{d t} = F(u)$, it is often the case that $F$ is equivariant under translations, i.e. that $T_\alpha F(u) = ...

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### Counting modular squares in an interval

For an integer $m$, let $S^m_{x_0,x_1} = \{ t | x_0 ≤ t ≤ x_1 $ and $t$ is a square modulo $m \}$. Let $S^m_x$ = $S^m_{0,x}$.
Determining whether the sets $S^m_x$ are empty is easy (1 is always a ...

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### What are the monoids in which every globally idempotent subsemigroup contains the identity element?

A semigroup is called globally idempotent when for any $x\in S$ there are $y,z\in S$ such that $x=yz$.
Is there a name for monoids whose every globally idempotent subsemigroup contains the identity ...

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### When does a power semigroup have a zero, and what can the zero be?

Let $S$ be a semigroup. The power semigroup of $S$ is the set $P(S)=2^S\setminus\lbrace\varnothing\rbrace $ with the operation $$AB=\lbrace ab\ |\ a\in A,\ b\in B\rbrace.$$
This operation is ...

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### How many binary operations are associative?

Let $X$ be a finite set of $n$ elements, and consider a binary operation $\odot: X \times X \rightarrow X$. There are $n^{n^2}$ such binary operations, as the $n \times n$ table entries can each
be ...

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### A linearly orderable monoid which does not embed into a linearly orderable group

It is known (after an example of A.I. Mal'cev) that there exist cancellative semigroups which do not embed into a group. On the other hand, it is not difficult to see that every linearly orderable ...

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### Equivalence between Algebraic Semi-group Structures and Coalgebra Structures for an Algebraic Variety?

I was looking at this old question
Hopf algebra and group structure correspondence for algebraic varieties
which says that there exists an equivalence between algebraic group structures on
an ...

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### On the notion of torsion-freeness in semigroup theory

The following seems to be the "official" notion of torsion-freeness in the context of semigroups:
TF1. A (multiplicatively written) semigroup $\mathfrak A$ is torsion-free if there do not ...

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193 views

### Strictly totally ordered semigroups - Looking for references

Let $\mathfrak A = (A, \cdot)$ be a semigroup (written multiplicatively). We say that $\mathfrak A$ is linearly orderable if there exists a total order $\le$ on $A$ such that $ac < bc$ and $ca < ...

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### What do we know about the semigroup $e^{it\sqrt{-\Delta}}$

I'm very interested in the properties of the semigroup $e^{it\sqrt{-\Delta}}$, it may has some fundamental differences(such as the kernel) with the well-known schrodinger semigroup $e^{it\Delta}$.
...

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### Reference for subsemigroups of $\mathbb{N}^n$

A well known result about the natural numbers $\mathbb{N}$ says that for any finite subset $A \subset \mathbb{N}$ there exists $R \ge 0$ such that if $n$ is in the subgroup of $\mathbb{Z}$ generated ...

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### Embedding Semigroups in Rings

Let $S$ be a finite commutative semigroup with identity. Under what conditions (on the semigroup $S$) it is possible to find a ring $R$ such that the multiplicative structure of $R - \{0\}$ is ...

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### Minimal right ideals in finite semigroup

Let $E$ be a finite semigroup. According to N. Bourbaki (Algèbre I p. 121 exerc. 14 c), if $M$ and $M'$ are minimal right ideals in $E$, then they are isomorphic. I spent some time browsing through ...

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### Is the universal inverse semigroup of a commutative semigroup an embedding?

The question of existence of a universal inverse semigroup of an arbitrary semigroup has been answered before (this is a construction similar to the Grothendieck group). Let's refer to the universal ...

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### Idempotent semigroups: Are they all residually finite?

As pointed out by Mark Sapir in his answer to a related question, every residually finite divisible semigroup is idempotent (hence uniquely divisible). On another hand, it is not difficult to prove ...

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### On a property of subsemigroups

Let $H$ denote a subsemigroup of a semigroup $G$.
I'm interested in the following property:
$$\forall g\in G\exists h\in H:gh\in H.$$
This property is weaker than the property that $H$ is an ideal ...

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### A semigroup with the property that $x^n = a$ has at least one solution

Is there a standard name for a (multiplicatively-written) semigroup $(A, \cdot)$ such that, given an arbitrary $a \in A$, the equation $x^n = a$ has at least one solution $x \in A$ for each $n \in ...

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### Is the class of inverse semigroups globally determined?

This question is a follow-up to this one I asked on math.stackexchange. I've decided to ask here because I believe this is a research-level question. I'm sorry if I'm wrong -- I'm not a researcher ...

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### Is there a general result that theorems about finite structures proved in ZFC can be proved in ZF?

The title question is too vague so let me be specific.
Much of modern finite semigroup theory uses profinite semigroups and properties of profinite semigroups that depend on the existence of prime ...

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### subsets of $\mathbb{R}^+$ closed under addition

No one's answered this question so here's a simpler question: Has anyone described or catalogued all sets of non-negative real numbers that are closed under addition? In particular, how about those ...

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### Which semigroups can be linearly ordered?

As usual I consider a semigroup to be a structure $(A, +)$ such that $+$ is an associative binary function over the set $A$. The notion of linearly-ordered semigroup corresponds to structures of the ...