The semigroups tag has no wiki summary.

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### Iterated sumset inequalities in cancellative semigroups

This question is motivated by the following well-known theorems:
Thm (Plünnecke): If $A$ is a finite nonempty subset of an abelian group, then for every $n$ we have $|A^n| \le ...

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### Coin problem with permutations

Let $a,b,c$ be positive integers with gcd$(a,b,c)=1$, and let $\mathbb{N}$ denote the set of nonnegative integers.
It is well known that $\mathbb{N} \setminus (a \mathbb{N}+b \mathbb{N} + c ...

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144 views

### Correspondence between numerical semigroups and polynomials?

A numerical semigroup $A$ is defined as a subsemigroup of the semigroup $(\mathbb{N},+)$ of the positive integers such that the set $\mathbb{N}\setminus A$ is finite. Equivalently (for a subsemigroup) ...

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297 views

### Computing the pro-solvable closure of a finitely generated subgroup of a free group

The pro-solvable topology on a group $G$ is the unique group topology such that the set of normal subgroups $N\lhd G$ with $G/N$ a finite solvable group is a fundamental system of neighborhoods of the ...

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95 views

### 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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235 views

### What is the pro-algebraic completion of the free semigroup on one generator?

This question is motivated by an attempt to understand what is going on in Tom's post from a certain point of view.
Let $\mathbb N^+$ be the free semigroup on one generator (so the positive natural ...

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123 views

### Certain conditions on cancellative semigroups

This is extracted from this question following Benjamin Steinberg's suggestion.
For a semigroup $S,$ let $P(S)$ denote the power semigroup of $S,$ which is made up of all non-empty subsets of $S$ ...

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114 views

### On the computational complexity of the Hilbert polynomial of numerical semigroup rings

Let $(R, \mathfrak{m}) = k[[X^a, X^b, X^c]]$, $a<b<c$, $gcd(a, b, c) = 1$, be a semigroup ring. We have $R$ is a Cohen-Macaulay local ring of dimension one. It is well known that ...

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### dual composition of binary relations

I'm not sure if this is of any interest at all, but I spent some time looking at it a couple of years ago so I'd like to ask for input on this.
Given two binary relations $\rho,\,\sigma$ on a set ...

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87 views

### Pseudovarieties of monoids

All (pseudo)varieties considered here are (pseudo)varieties of monoids.
It is known that any (finite or infinite) monoid that satisfies the identities
\begin{equation}
xhxyty = xhyxty, \quad ...

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### Number of k-generated semigroups

Given some $k>1$, I am interested in the number of $k$-generated semigroups of order $n$ (either up to isomorphism or all associative binary operations on an n-element set). At first I thought ...

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136 views

### Orbit-Stabilizer theorem for continuous groups

The orbit-stabilizer relationship (also known as the orbit-stabilizer theorem) is very clear for finite groups. Is there an equivalent relation for continuous groups?
Also, is there a similar notion ...

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151 views

### What is the combinatorial data classifying non-normal affine toric varieties?

Recall that a toric variety is a variety $V$ containing an open dense algebraic torus. Here an algebraic torus means a finite product of copies of the multiplicative group of the ground field (which I ...

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151 views

### 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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71 views

### 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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113 views

### 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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257 views

### Is there a homological way to compute quiver presentations?

I have recently been studying with colleagues the representation theory of certain finite monoids that come up in probability theory and combinatorics, see Ken Brown's beautiful survey here.
These ...

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46 views

### Terminology for torsion semigroups where the order of elements is uniformly finite

A (multiplicatively written) semigroup $\mathbb A = (A, \cdot)$ with the property that ${\rm ord}_\mathbb{A}(a) := |\{a^n: n \in \mathbf N^+\}| < \infty$ for every $a \in A$ is called a periodic ...

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171 views

### Standard name for a Monoid/Semigroup with $a+b \leq a, b$?

I have seen suplattice and inflattice being used when dealing with a lattice. What about when you don't have a lattice?
For instance, for reals $a,b > 0$, define $$a \oplus b = ...

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114 views

### Non-finitely based varieties and pseudovarieties

The variety of semigroups defined by $B=\Big\{(x^py^p)^2=(y^px^p)^2:p \text{ is prime}\Big\}$ is non-finitely based (Isbell, 1970). Is the pseudovariety defined by $B$ also non-finitely based?
More ...

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130 views

### On the infinitesimal generator of a 1-dimensional stochastic heat equation: core and explicit form

Denote $E = C([0, 1])$. I am consider a 1-dimentional stochastic heat equation on $h$:
$\partial_tu(t, x) = \partial_x^2u(t, x) - V'(u(t, x)) + \dot{W}(t, x)$, for all $(t, x) \in (0, ...

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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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248 views

### 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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61 views

### Semigroup solution via Lumer-Phillips

Let $a$ be a coercive, bounded bilinear form on $H^1(\Omega)$, where $\Omega$ is some sufficiently "nice" region. I defined an operator $A:H^1(\Omega)\mapsto H^1(\Omega)^*$ by:
$$
...

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42 views

### Goldie's Theorem for Semigroups

Goldie's theorem is a theorem in noncommutative ring theory that gives a clear picture of semiprime Noetherian rings (actually a slightly broader class). Let $R$ be a semiprime Noetherian ring. The ...

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194 views

### Estimating the kernel of Poisson semigroup $e^{-z\sqrt{-\Delta}}$ for complex $z$

Let $f(z,a)$ be an analytic function on $C^+=\{\Re z>0\}$ for each fixed $a>0$, and we have the following (weaker) estimates
$$
|f(re^{i\theta},a)|\leq C (r\cos\theta)^{-n}, ...

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### Lower periodic subsets of groups and semigroups

Suppose that $A$ and $B$ are subsets of a group or semigroup. We call $A$ left
upper [resp. lower] $B$-periodic if $BA\subseteq A$
[resp. $A\subseteq BA$]. If $A$ is both left upper and
lower ...

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71 views

### Semigroups on Banach Lattice

Let $\{Z(t)\}_{t\geq 0}$ be a semigroup of positive operators on a Banach lattice $X$. I want to show that
$$\int_0^1[Z(1-s)+Z(1+s)]fds-f\in X_+,\quad f\in X_+$$
Where $X_+$ denotes the positive ...

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143 views

### Classification of rings between a PID and its field of fractions?

Let $D$ be a PID and let $\mathrm{Frac}(D)$ be its field of fractions. I want to classify the intermediate rings $D\subseteq R\subseteq \mathrm{Frac}(D)$.
Theorem: Every such ring $R$ is a ...

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64 views

### 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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### 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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47 views

### Decomposition results for locally commutative semigroups

Every finite abelian group is the direct product of its cyclic groups of prime order, and every commutative monoid divides a product of its cyclic submonoids. Could these results generalized to ...

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65 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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### semigroup actions of groups on regular rooted trees

If $G$ is a group which has a semigroup action on a regular rooted tree via prefix-preserving, continuous transformations (I give the tree the path metric), what kinds of algebraic restrictions can we ...