The semigroups tag has no usage guidance.

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**1**answer

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### Restriction of a semigroup to a form domain

Say, we have a Hilbert space $H$ with a semibounded self-adjoint
operator $A:D(A)\to H$ generating a strongly continuous semigroup
$T(t):H\to H$. Is it possible to restrict $T(t)$ to a form domain of ...

**0**

votes

**1**answer

74 views

### Solutions of an nonlinear evolution problem

We consider the following continuous-time nonlinear evolution problem
\begin{equation}
\begin{cases} \dot{y}(t)=Ay(t)+F(y(t),u(t)),\quad t\geq0\\y(0)=f\in\mathcal{X}\end{cases}
\end{equation}
where ...

**0**

votes

**1**answer

102 views

### Maximal group image!

How to prove that if S is a finitely generated Clifford semigroup its maximal group image is actually the S_{e_{n}}?

**0**

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**0**answers

75 views

### semigroups regular!

I am trying to prove that if a maximal group image G(S) of a Clifford semigroup S, is abelian-by-finite does the Clifford semigroup S is abelian-by- finte?

**3**

votes

**1**answer

656 views

### 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 ...

**7**

votes

**1**answer

189 views

### 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 ...

**0**

votes

**0**answers

57 views

### Is there a general theory for the structure of the (semi)group generated by morphisms of an affine space $F_p^3$?

Consider an affine space $\mathbb{F}_p^3$, and assume we have a handful of morphisms $f_i : \mathbb{F}_p^3 \rightarrow \mathbb{F}_p^3$ given by $$f_i(x, y, z) =(P_i(x, y, z), Q_i(x, y, z), R_i(x, y, ...

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48 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 ...

**5**

votes

**1**answer

281 views

### $C_0$-semigroups applications

My graduation thesis was about stability theorems for $C_0$-semigroups (see the Wikipedia article for the definitions: http://en.wikipedia.org/wiki/C0-semigroup). I would like to know if there is ...

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vote

**0**answers

62 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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votes

**1**answer

65 views

### Infinitesimal generator is bounded [closed]

Consider a strongly continuous semigroup of bounded linear operators $S(t):X\to X$. The infinitesimal generator of $S(t)$ is the linear operator $A:D(A)\subseteq X \to X$ defined by
...

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votes

**1**answer

163 views

### Contraction semigroup

Let $(X, \mu)$ be a finite measure space and let $A$ be a non-negative self-adjoint operator which generates a contraction semigroup $e^{tA}$ on $L^2(X, \mu)$. If additionally, we have that $e^{tA}$ ...

**4**

votes

**1**answer

163 views

### Sets of natural numbers such that sums of a bounded number of its elements form a semigroup

This is a naive question and I'm afraid it might be better placed on math.se. I would like to leave it to your judgement.
I would like to know what is known about sets $A$ of natural numbers such ...

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vote

**0**answers

43 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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votes

**1**answer

830 views

### Who coined “mob” and “clan” and why these words?

A mob is a word used for a topological semigroup which is a Hausdorff space. A clan is a compact connected mob with a two-sided identity element.
Who used these words with these meanings first and ...

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votes

**0**answers

134 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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vote

**0**answers

202 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}, ...

**4**

votes

**1**answer

245 views

### Cancellable elements of a power semigroup

For a semigroup $S,$ its power semigroup $P(S)$ is the semigroup of all non-empty subsets of $S$ with the operation given by $AB=\{ab\,|\,a\in A,b\in B\}.$ I would like to know about the cancellable ...

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**3**answers

956 views

### Non-abelian Grothendieck group

By general nonsense the forgetful functor from groups to monoids has a left adjoint. It maps a monoid $(X,\cdot,1)$ to the free group on $\{\underline{x} : x \in X\}$ modulo the relations ...

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**0**answers

115 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 ...

**5**

votes

**2**answers

273 views

### 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 ...

**1**

vote

**1**answer

86 views

### Non-idempotent ultrafilters in the Stone-Cech compactification

Supposing that $\Gamma$ is an infinite, discrete group and that $\beta\Gamma$ is the Stone-Cech compactification of $\Gamma$, the group structure of $\Gamma$ can be extended to a semigroup structure ...

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**0**answers

86 views

### 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 ...

**1**

vote

**0**answers

68 views

### 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 ...

**3**

votes

**1**answer

63 views

### Cosets of the fixer of an action of a monoid on a finite set

Let $M$ be a monoid that acts transitively from the right on a finite set $X$.
Assume furthermore that the action of $M$ on $X$ induces for every $m \in M$ a bijection on $X \to X, x \mapsto x.m$.
Let
...

**3**

votes

**1**answer

257 views

### submonoid of a matrix monoid with a common eigenvector

Hello,
I am considering two real invertible $3\times 3$ matrices $A$ and $B$ and a nonzero vector $v\in\mathbb{R}^3$ and i am wondering if the submonoid $E$ of the monoid $(A,B)$ genererated by $A$ ...

**3**

votes

**0**answers

88 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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votes

**1**answer

95 views

### $C_0$ semigroups on parameterized Banach spaces or moving domains

Is there any literature corresponding to one or two-parameter semigroups such that eg. $T(t) \in \mathcal{L}(X(t))$ or $T(s,t) \in \mathcal{L}(X(t),X(s))$ for parameterized Banach spaces $X(t)$???
I ...

**4**

votes

**0**answers

298 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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votes

**2**answers

146 views

### a question about semigroups

Let $S$ be a semigroup and $I,J$ be two ideals of $S$. For a semilattice we know that $IJ=I\cap J$. Now the question is there a semigroup with the property $IJ=I\cap J$. thanks for your attention

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**0**answers

74 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 ...

**3**

votes

**1**answer

195 views

### Cancellative semigroup on a distributive lattice

Let $(S,\le)$ be a distributive lattice. Is there a semigroup structure on $S$ such that $S$ is cancellative and always $(x\wedge y)(x\vee y)=xy$?

**5**

votes

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240 views

### Locally finite varieties which are not finitely generated

Let $\Sigma$ be a signature consisting of operations with finite arity. Let $\mathcal{V}$ be a variety of algebras for this signature. Further suppose that $\mathcal{V}$ is locally finite i.e. every ...

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votes

**2**answers

202 views

### What's the current state of one-rule semi-Thue system termination problem?

What's the current state of one-rule semi-Thue system termination problem? Search produces a lot of references, but it's hard to find out if decidability of this problem has been proven or not.

**2**

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**0**answers

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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votes

**3**answers

668 views

### Reference on Semigroup Theory and Parabolics PDE'S

Recently started to study Semigroup Theory. My background is equivalent to the first three chapters of the Jack Hale's book, Asymptotic Behavior of Dissipative Systems.
Looking for a reference to an ...

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votes

**2**answers

314 views

### Lecture notes on semi group theory for linear evolution equations

I am reading (or trying to read :)) One parameter semigroups for Linear Evolution equations by Klaus-Jochen Engel and Rainer Nagel. I was wondering if someone was aware of a good set of lecture notes ...

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votes

**3**answers

416 views

### Haar Measure on Locally Compact Semigroups

I'm reading on Haar measure and we know that every locally compact group admits a Haar measure, is the same true for semigroups? if not, is there a class of semigroups that admits a Haar measure?
...

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votes

**3**answers

504 views

### Is there a general notion of semigroup action?

The analogous result to Cayley’s theorem or Yoneda lemma in semigroup theory represents semigroups as semigroups of functions from a set to itself. This suggests that a semigroup action consists of a ...

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**0**answers

115 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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vote

**1**answer

242 views

### A property of groups of operators

Let $X$ be a Banach space. We consider the evolution equation:
$$x'(t)=Ax(t), \ \ \ \ \ \ \ t\in \mathbb{R},$$
where $A$ is a bounded operator.
I know that if $X=\mathbb{R^n}$ and $A$ is a matrix, ...

**0**

votes

**2**answers

117 views

### Using group presentation for its corresponding semigroup?

Somewhere Colin M. Campbell noted:
If $A$ is a semigroup defined as $$A=Sg(\pi)=\langle a_1,\cdots, a_d\mid u_1=v_1,\cdots,u_e=v_e\rangle $$ then the same generators with the same relations can ...

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**1**answer

179 views

### Is the monoid of taking iterated images and inverse images freely generated by the image and inverse image operation?

Let $\mathcal{F}$ denote the class of all functions. Let $U,L:\mathcal{F}\rightarrow\mathcal{F}$ denote the mappings where if $f:X\rightarrow Y$, then $U(f):P(X)\rightarrow P(Y),L(f):P(Y)\rightarrow ...

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**0**answers

142 views

### 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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91 views

### Semidirect products of semigroups [closed]

Let $S,T$ be two semigroups. A function $f:S\to T$ is called multiplicative if for any $x,y\in S$ we have $f(xy)=f(x)f(y)$. If $T=S$ then $f:S\to S$ is called automorphism on $S$.
A function ...

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votes

**1**answer

386 views

### Are semigroups with finite-to-one right multiplication “moving”?

A semigroup $S$ is moving if $S$ is infinite, and for all finite
$F\subseteq S$ and infinite $A\subseteq S$, there are $a_{1},\dots,a_{k}\in A$ such that,
for all but finitely many $s\in S$,
$$
...

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**1**answer

127 views

### A question about uniformly bounded semigroups

Let $A$ be an unbounded linear operator of domain $D(A)$ defined on a Banach space $X$. Suppose that $A$ generates a $C_0$-semigroup $T(t)$ which is uniformly bounded. I would like to know if there ...

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votes

**1**answer

330 views

### About the convergence rate for an approximation to the heat kernel

Let $G(t,x)$ be the heat kernel
$$
G(t,x)=\frac{1}{\sqrt{2\pi t}}e^{-\frac{x^2}{2t}}, \quad t>0, \:x\in\mathbb{R}.
$$
Here is one approximation to $G(t,x)$:
$$
G_\epsilon(t,x)=e^{-t/\epsilon} ...

**3**

votes

**1**answer

135 views

### Integral representation of the resolvent of a semigroup

Let $T(t)$ be a $C_{0}$-semigroup with the generator $A$. Now, does the so called integral representation of the resolvent
$$
(\lambda - A)^{-1} = \int_{0}^{\infty} e^{-t\lambda}T(t) dt
$$
hold for ...