# Questions tagged [semigroups-and-monoids]

A semigroup is a set $S$ together with a binary operation that is associative. Examples of semigroups are the set of finite strings over a fixed alphabet (under concatenation) and the positive integers (under addition, maximum, or minimum). A monoid is a semigroup with a neutral element. Of course, any group is also a monoid/semigroup.

554 questions
Filter by
Sorted by
Tagged with
113 views

### When is semigroup algebra local?

Let $G$ be a finite semigroup (or monoid if that helps) and $K$ a field. Question: When is the semigroup algebra $KG$ local? Here local means that there is a unique maximal right (or left) ideal. ...
127 views

### Cartan matrix of the full transformation monoid ring

Let $T_n$ be the full transformation monoid of an $n$-set and $A_n=KT_n$ its monoid algebra over the complex numbers. Question 1: Is the Cartan matrix of $A_n$ known? Im especially interested to see ...
344 views

### Algebra generated by transformation matrices

Let $T_n$ be the full transformation monoid of an $n$-set $N_n$ with elements 1,...,n consisting of all functions $f: N_n \rightarrow N_n$. We can associate to each function $f$ a matrix $M_f$ in the ...
148 views

1 vote
42 views

### Neighborhoods of idempotents in topological inverse semigroups

In a topological group, for any neighborhood $U$ of the origin, there is another such neighborhood with the property that $V.V\subseteq U.$ I conjecture a similar property for topological inverse ...
146 views

### Making the powerset into a topological monoid

Every monoid $X$ induces a monoid structure $\circledast$ on $\mathcal{P}(X)$ via $$U\circledast V := \{uv\ |\ u\in U,v\in V\}.$$ Moreover, a morphism of monoids $f\colon X\to Y$ induces a morphism of ...
1 vote
80 views

### Eventual stabilization for repeatedly adding multiplayer games

This question is an outgrowth of a couple previous questions of mine. In order: 1,2,3. This should be fully self-contained, but those questions may help motivate this one. To keep things readable, I'...
180 views

### Usefulness of total algebras and exotic generating series

In his first Algebra volume, Bourbaki  defines the structure of a “total algebra” i.e. the space of functions on a monoid $M$ (to a ring $k$) with the convolution product ( a function $f:\ M\to k$ ...
200 views

### Monoid associated to $>2$-player Hackenbush

There is some literature on multiplayer combinatorial game theory, but as far as I can tell none of it follows the line of attack below. I'd love a pointer to a similar approach taken in the ...
131 views

### Examples of groups with a positive homogeneous presentation without the Haagerup property or not of type $F_\infty$

I am looking for groups with a certain presentation that do not have the Haagerup property or are finitely presented but not of type $F_\infty$ (meaninig that for some $n\geq 3$ we cannot find any ...
66 views

40 views

### Polyextremal groups

A polynomial of a semigroup $X$ is a function $f:X\to X$ of the form $f(x)=a_0xa_1\cdots xa_n$, where $a_0,a_1,\dots,a_n$ some elements of the semigroup $X^1=X\cup\{1\}$, called the coefficients of ...
1k views

### The number of polynomials on a finite group

A function $f:X\to X$ on a group $X$ is called a polynomial if there exist $n\in\mathbb N=\{1,2,3,\dots\}$ and elements $a_0,a_1,\dots,a_n\in X$ such that $f(x)=a_0xa_1x\cdots xa_n$ for all $x\in X$. ...
1 vote
49 views

122 views

### Automorphisms of special egg-box diagrams

By a egg-box diagram I will simply mean a (possibly infinite) rectangular array of holes, with some of the holes containing an egg (denoted by a filled-in circle) and the rest of the holes are empty (...
1 vote
93 views

### On the maximum elements of a numerical semigroup that have order between $n$ and $2n$

Let $S$ be a submonoid of the non-negative integers $\mathbb Z_{\geq 0}.$ If $\mathbb Z_{\geq 0} \setminus S$ is finite, we say that $S$ is a numerical semigroup. Let $S^*$ denote the collection of ...
84 views

### What are the n-ary subsemigroups of $\mathbb{N}$?

There is a well-known result about the subsemigroups of $\mathbb{N}$ stating that the additive subsemigroup generated by a (finite) set $A$ of $\mathbb{N}$ is cofinite in $\mathbb{N}$ if and only if \$\...