The semigroups tag has no wiki summary.

**7**

votes

**2**answers

382 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 ...

**7**

votes

**2**answers

308 views

### 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 ...

**3**

votes

**2**answers

434 views

### 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 ...

**4**

votes

**2**answers

555 views

### 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 ...

**8**

votes

**3**answers

625 views

### What is the smallest variety of algebras containing all fields?

A field is a ring whose nonzero elements form a commutative group under multiplication. A field is also a commutative inverse semigroup with respect to multiplication. The unique multiplicative ...

**3**

votes

**0**answers

252 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 ...

**3**

votes

**2**answers

458 views

### Do these kernel functions satisfy the semi-group property?

Dear Friends,
Define the kernel functions for $a\ge 1$,
$$
G_a(t,x) := \frac{C_a t}{t^{1+1/a}+|x|^{1+a}}, \qquad \forall t>0,\: x\in R\;,
$$
where the constant $C_a$ is some normalization ...

**20**

votes

**2**answers

636 views

### Mapping from a finite index subgroup onto the whole group

Dear All,
here is the question:
Does there exist a finitely generated group $G$ with a proper subgroup $H$ of finite index, and an (onto) homomorphism $\phi:G\to G$ such that $\phi(H)=G$?
My guess ...

**12**

votes

**2**answers

834 views

### Economical hard word problem

Can anyone give me an example of a very simple word problem, where by "simple" I mean that it has very few generators and relations, that is nevertheless insoluble. To make the question easier, I am ...

**4**

votes

**0**answers

233 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 ...

**2**

votes

**1**answer

247 views

### Is there existing terminology for this technical condition on semilattices?

Given a semilattice $S$, a subset $E$, and a positive integer $n$, let $E^{[n]}$ be the set of all products of $n$-tuples in $E$. Thus $\bigcup_{n\geq 1} E^{[n]}$ is nothing but the subsemigroup of ...

**7**

votes

**1**answer

647 views

### How is called a semigroup…

Does anyone know, how is called a semigroup in which every equation $ax=b$ has only a finite set (maybe empty) of solutions?

**3**

votes

**1**answer

450 views

### Study of free monoids of the recursive S. Eilenberg.

Compared to the usual treatises on recursion (eg, Rogers H. "Computability and Undecidability." McGraw-Hill, New York) the book of Samuel Eilenberg & Calvin C. Elgot "Recursiveness" treats such ...

**3**

votes

**1**answer

253 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 $A$ ...

**5**

votes

**3**answers

636 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 ...

**0**

votes

**0**answers

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 ...

**1**

vote

**1**answer

192 views

### The intersection of Block Groups and R-trivial (finite) monoids

Let $\textbf{BG}$ be the pseudovariety of block groups, also known as $\textbf{EJ}, \textbf{PG},\ldots,\text{etc.}$(see [1]), and let $\textbf{R}$ be the pseudovariety of R-trivial monoids, by the ...

**6**

votes

**1**answer

196 views

### Positive cone of a subgroup of Z^n

This question sounds like it should be very well known, but for some reason I failed to find a decent answer anywhere. Let $G\subset\mathbb{Z}^n$ be a subgroup, and $G_+=G\cap\mathbb{Z}_{\ge0}^n$ be a ...

**8**

votes

**1**answer

472 views

### Magma “actions” (or alternatively, “What is the Yoneda lemma for magmas?”)

Arguably the most import thing about groups, semigroups and more generally categories, is that they can act on sets (or even collections of sets in the case of a category). This is the basis for all ...

**5**

votes

**2**answers

510 views

### Do all finitely generated nilpotent semigroups have polynomial growth?

The notion of nilpotency passes nicely from groups to semigroups. Define $q_1(x,y)=xy$ and $$q_{i+1}(x,y,z_1,\cdots,z_i)=q_i(x,y,z_1,\cdots,z_{i-1})z_iq_i(y,x,z_1,\cdots,z_{i-1})$$ inductively for all ...

**2**

votes

**1**answer

229 views

### Nuclearity of certain semigroup crossed product C*-algebras

This question is related to this question link.
Suppose we have an (abelian) semigroup $S$ acting by endomorphisms on a $C^*$-algebra A giving rise to a semigroup crossed product $B = A\rtimes S$. ...

**5**

votes

**1**answer

427 views

### an example of a semigroup with solvable word problem but unsolvable power problem

We say that a semigroup $S$ has solvable power problem if there is an algorithm that takes as input an element $s \in S$ and decides whether or not there exist $m,n \in \mathbb{N}$ with $m \neq n$ and ...

**5**

votes

**1**answer

456 views

### Percolation in Cayley graphs of semigroups.

Percolation in Cayley graphs of groups are studied by many researchers. There are also the concept Cayley graphs for semigroups. Are there any research about percolation in Cayley graphs for ...

**0**

votes

**1**answer

130 views

### Small set of acts over a countable monoid?

Given a countable monoid $S$, is the set of all (isomorphic representatives of) $S$-acts a small set?

**1**

vote

**1**answer

122 views

### undecidability in the dynamics of functions $f: \Sigma^* \rightarrow \Sigma^*$

Does anyone know any undecidable problems in the dynamics of functions (not necessarily monoid homomorphisms or anything) from \Sigma^* to \Sigma^* where \Sigma is a finite set? In particular, I'm ...

**14**

votes

**12**answers

2k views

### Why semigroups could be important?

There is known a lot about the use of groups -- they just really appear a lot, and appear naturally. Is there any known nice use of semigroups in Maths to sort of prove they are indeed important in ...

**6**

votes

**2**answers

288 views

### need references regarding the elementary theory of free semigroup and free abelian groups

Recently, I read that two free abelian groups $S$ and $T$ have the same elementary theory if and only if rank$S$=rank$T$. Does anyone have a reference with a proof of this? Also, what is known about ...

**4**

votes

**1**answer

253 views

### semigroups acting as continuous functions on regular rooted trees

Let $T$ be a regular rooted tree. Make $T$ into a metric space by making each edge isometric to the unit interval. What is known about what semigroups can act as continuous functions on $T$ such ...

**9**

votes

**3**answers

504 views

### The concept “conjugate class” in monoids.

Is there any concept in monoids that is similar to the concept "conjugate class" in groups? For example, are there any such similar concept in symmetric inverse monoids? Thank you very much.

**0**

votes

**1**answer

252 views

### A Nomenclature Issue : Imprimitive Semigroup?

The following question was asked by me on the forum sci.math.research,
“An imprimitive group is a transitive permutation group with a non-trivial
equivalence relation compatible with the action of ...

**4**

votes

**2**answers

380 views

### examples of finitely generated semigroups that are not residually finite

Does anybody know of any finitely generated semigroups that are not residually finite and whose group of units (if there is an identity) is trivial? Basically, I'm looking for finitely generated ...

**1**

vote

**1**answer

367 views

### Transitive Semigroups of $2\times 2$ matrices

Suppose $G$ is a semigroup (i.e., closed under matrix multiplication) of invertible $2\times 2$ real matrices. Suppose also that $G$ is transitive i.e., for any two non-zero vectors $u$ and $v$ there ...

**0**

votes

**2**answers

295 views

### Is this a pre-ordered commutative semigroup?

Motivation
I'm studying an approach to axiomatic thermodynamics based on the notion of commutative semigroup $(S,+)$ with a preorder relation $\to$ on $S$. In other words, $S$ is non-empty set, the ...

**1**

vote

**2**answers

268 views

### reference for weak*-semigroup

Let $X$ a dual Bancah space (there exists a Banach space $Y$ such that $X=Y'$).
A weak* semigroup on $X$ is a semigroup $(T_t)_{\geq 0}$ on $X$ such that, for all $x\in X$, we have ...

**4**

votes

**2**answers

352 views

### Membership problem in monoids

What is the simplest example of a monoid with undecidable membership problem? In other words, I'm looking for a concrete monoid $S$ such that there is no algorithm which takes elements $s_1,...,s_n$ ...

**2**

votes

**2**answers

243 views

### what conditions can one place on a finitely generated periodic semigroup that will ensure the semigroup is finite?

I am not familiar with much semigroup theory, but this question came up in my research and I've been unable to find much on it.

**3**

votes

**1**answer

321 views

### Residual finiteness of groups versus residual finiteness of semigroups

A group $G$ is residually finite if, for any two elements $g$ and $g^\prime$ in $G$, there is a finite group $G^\prime$ and a (group) homomorphism $f: G \rightarrow G^\prime$ such that $f(g)$ doesn't ...

**5**

votes

**1**answer

330 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 ...

**3**

votes

**2**answers

352 views

### What is the relation between the number syntactic congruence classes, and the number of Nerode relation classes?

For a monoid $M$ and a subset $S$ of $M$, define the syntactic congruence $\equiv_S$ of $S$ as the least congruence on $M$ that saturates $S$, i.e. :
$$u \equiv_S v \Leftrightarrow (\forall x, y)[xuy ...

**1**

vote

**1**answer

235 views

### Vocabulary on monoid periodicity

I'm learning about periodic languages, and I'm confused over the vocabulary used to describe the periodicity of (syntactic) monoids.
If I understand correctly, a monoid M is periodic if :
$$(\forall ...

**12**

votes

**1**answer

1k views

### Do these conditions on a semigroup define a group?

As is well known, if $S$ is a semigroup in which the equations $a=bx$ and $a=yb$ have solutions for all $a$ and $b$, then $S$ is a group. This question arose when someone misunderstood the conditions ...

**0**

votes

**2**answers

159 views

### small extensions of the free semigroup of rank 1

Let N denote the free semigroup of rank 1. Say that a semigroup T is a small extension
of N if N embeds in T and |T - N| is finite. Is there some kind of classification
of small extensions of N? ...

**1**

vote

**1**answer

173 views

### Is the semigroup M(n, Z) finitely presented? If so, where can I find a presentation of it?

I am new to semigroup research, so I apologize if this is an easy question.

**1**

vote

**2**answers

345 views

### Relations in matrix semigroups

Suppose that $A_1, \dots, A_k \in M_n(\mathbb{Q})$ and $S$ is the semigroup generated by them. Two questions: are there always a finite set of relations $\{R_i\}$ among the $A_j$ such that $S$ is ...

**6**

votes

**2**answers

306 views

### Wants: Polynomial Time Algorithm for Decomposing a Multiset of Rationals into Two Additive Subsets.

First, allow me to say that this problem was posed to me by a professor in the department. It is related to his research in a way that I do not know. However, since I couldn't come up with anything ...

**4**

votes

**2**answers

453 views

### Normality of an affine semigroup

An affine monoid is a finitely generated commutative submonoid of $\mathbb Z^k$ for some positive integer k. Let S be an affine monoid and let G(S) be the group generated by S. We say the monoid S is ...

**3**

votes

**3**answers

330 views

### Representations of finite commutative band semigroups

I think it's clear that commutative semigroups S that are also bands, i.e. $e^2 = e$ for all e, correspond to finite posets (consider the elements of the semigroups as sets, where the intersection of ...

**9**

votes

**5**answers

638 views

### References/literature for pushouts in category of commutative monoids? [ed. - amalgams]

This is more of a request for pointers to relevant literature than a question per se. I am, erm, looking at a paper which uses a kind of iterated pushout construction to obtain a commutative monoid ...

**8**

votes

**5**answers

884 views

### Examples of left reversible semigroups

I am looking for concrete examples of cancellative, left reversible semigroups. Left reversible semigroups are also called "Ore semigroups". See this wikipedia page for the definition of a left ...

**4**

votes

**1**answer

267 views

### One-parameter semigroups of bimodules

Suppose M is a von Neumann algebra.
Consider a monoidal category of bimodules over M.
Here a bimodule is a Hilbert space with two normal representations of M.
The monoidal structure is given by ...