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265 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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82 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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212 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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97 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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111 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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116 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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115 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

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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68 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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108 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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235 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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93 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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101 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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59 views

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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239 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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95 views

Standard name for a Monoid/Semigroup with a+b <= 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 positive reals a, b define a |+| b === 1/((1/a) + (1/b)), you ...
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66 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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117 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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57 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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85 views

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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67 views

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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49 views

Semigroups admitting generating sets which induce a “weight” on elements of the semigroup

Neither universal algebra nor semigroup theory is something I really know much about, so this question might not be appropriate for MO; if so, I'll move it to MSE. Recently, I've been playing ...
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42 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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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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167 views
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154 views

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 ...