The semigroups tag has no wiki summary.

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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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57 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 ...

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**1**answer

338 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 ...

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42 views

### Example of A semigroup with a unique left invariant measure

I'm looking for an example of a locally compact semigroup that has a unique left invariant measure.
I know that every locally compact group will admit a unique left invariant measere namely the Haar ...

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53 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
...

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125 views

### Semigroups with group like behavior

I'm trying to generalize some results done to groups to the semigroup case. I noticed that the results will not work with a general semigroup, I decided to try to extend the results to the inverse ...

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240 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 $A$ ...

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### 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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90 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 ...

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172 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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143 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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66 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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**1**answer

164 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 $(x\wedge y)(x\vee y)=xy$?

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175 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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132 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.

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### 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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575 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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155 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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317 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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356 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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104 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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233 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, ...

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### 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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173 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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### 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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107 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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### 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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367 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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### 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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120 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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### Measure generated by Semigroup $\exp[-t|p|]$

I am studying Ingrid Daubechies' paper 'An Uncertainty Principle for Fermions with Generalized
Kinetic Energy'.
On page 514, the measure $\mu_{x,y;t}$ is introduced as generated by the semigroup ...

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322 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} ...

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### 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 ...

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### Embedding a linearly ordered free monoid into a linearly ordered group

A linearly ordered (shortly, l.o.) monoid is a triple $\mathbb M = (M, \cdot, \le)$ for which $(M, \cdot)$ is a (multiplicatively written) monoid and $\le$ is a total order on $M$ such that $xy < ...

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### Variety of commutative semi group [closed]

V is a variety of commutative semi group satisfying the identity $x^2 = x^3$.
I need to prove that:
$|F_V(\{x_1\dots,x_n\})|$ = $3^n -1$.
Any hints on this ?
$F_V$ is V-free algebra.

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355 views

### 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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268 views

### I need following books (soft copies) [closed]

I know this is not the place to ask for such help, but I cant find these books in my country and not even on line and the shipping is very expensive. If someone out there have any of these books (soft ...

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### 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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### 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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### Examples of cancellative normal semigroups

I've got a couple of things to test against normality in cancellative semigroups. A normal semigroup $S$ is one in which for any $x\in S$ we have $xS=Sx.$ This implies the Ore condition $$x,y\in ...

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### Terminology for the equation $a=a+b$ in commutative semigroups

Let $(S,+)$ be a commutative semigroup. For $a,b\in S$ consider the equation $a=a+b$. Does such a relation between the given $a$ and $b$ have a name? I am currently using such equations quite often ...

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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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243 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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### Does the generator of a 1-parameter group of Banach space isometries know which elements are entire?

Let $X$ be a complex Banach space. Let $(\sigma_t)_{t \in \mathbb{R}}$ be a 1-parameter group of linear isometries of $X$ which is strongly continuous i.e. $t \mapsto \sigma_t(x)$ is continuous for ...

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325 views

### Representations of products of groups (and monoids)

I have very little knowledge of representation theory, but the following has come up in my summer undergrad research project (relates to conformal field theory and geometric function theory).
Suppose ...

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123 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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### what is the meaning of the operator $ EXP[\frac{ \theta }{2}\frac{\partial^2}{\partial \overrightarrow{v}^2}]$

the name of this operator is one-parameter semigroup
for example $ EXP[\frac{ \theta }{2}\frac{\partial^2}{\partial \overrightarrow{v}^2}]f$，
$ f$is the function of $\overrightarrow{v}$
what is ...

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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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### Is irreducibility sufficient for uniqueness of invariant distribution for a Feller Semigroup?

Let $(T_t)$ be a strongly continuous semigroup of positive operators on $C(K)$, where $K$ is a compact space. Assume also that $T_t1 =1 $ for every $t\geq 0$.
(This is also called a Feller Semigroup.)
...

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200 views

### positive semigroups and convex operator

Let $\{Z(t)\}_{t\geq 0}$ be a strongly continuous positive semigroup on a Banach lattice V. (endowed with ordering $\leq$). $\phi:V\rightarrow V$ is a convex operator. I want to prove that ...