The tag has no wiki summary.

learn more… | top users | synonyms (1)

4
votes
0answers
214 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
1answer
238 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
1answer
639 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
1answer
444 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
1answer
227 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
3answers
559 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
0answers
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
1answer
184 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
1answer
190 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
1answer
441 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
2answers
474 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
1answer
224 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
1answer
414 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
1answer
453 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
1answer
128 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
1answer
121 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
12answers
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
2answers
281 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
1answer
252 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
3answers
477 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
1answer
246 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
2answers
363 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
1answer
366 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
2answers
285 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
2answers
253 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
2answers
344 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
2answers
237 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
1answer
312 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
1answer
322 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
2answers
306 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
1answer
229 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
1answer
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
2answers
157 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
1answer
164 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
2answers
333 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
2answers
301 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
2answers
443 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
3answers
319 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
5answers
625 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 ...
7
votes
5answers
796 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
1answer
263 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 ...