# Questions tagged [semigroups]

A semigroup is an algebraic structure consisting of a set together with a single associative binary operation. A semigroup with an identity element is called monoid. This tag is most frequently used for questions related to the concept of semigroups in the context of abstract algebra/universal algebra. Please use the more specific tag (semigroup-of-operators) whenever appropriate.

816 questions
Filter by
Sorted by
Tagged with
37 views

### an infinite monoid that is not free monoid and does not contain any free monoid [duplicate]

Let $H$ generated by some generators $H=\langle h_1, \ldots, h_n\rangle$ $(n\gt 1)$. My question is whether there exists any monoid $H$ such that $H$, is infinite and $H$ is not a free monoid and $H$ ...
22 views

### How can i create a Rees-matrix semigroup?

I've already read the definition of Rees-matrix semigroups, but I still can not imagine how to create one. For example.: I shall create a M(G;I;Lambda;P) semigroup where G is a group with 2 elements, ...
44 views

### How do we call a semigroup $I$ with a partial order $\le$ such that $t-s\in I$ for all $s,t\in I$ with $s\le t$? [closed]

If I have a semigroup $I$, which is a subset of a group $G$, and a partial order $\le$ on $I$ such that $t-s\in I$ for all $s,t\in I$ with $s\le t$, is there a special name for $I$? It is something ...
34 views

### Embedding a semigroup into a monoid

I have just started learning about groups and rings and I'm stuck on one exercise. I don't understand what $S^u$ really is and don't know where to start. So if anybody could help me with it, it would ...
74 views

### infinite monoid H that is not a free monoid and contains a free monoid as a submonoid [closed]

Let $H= \langle h_1, \ldots , h_n \rangle$ ($n>1$) be an infinite monoid that is not a free monoid. Does $H$ contain an isomorphic copy of a free monoid as a submonoid? EDIT. It is a natural ...
65 views

### Subsemigroup of free semigroup that is not free

Is there any example of subsemigroups of a free semigroup, for exemple of $(\mathbb{N}^*,\times)$ generated by primes, that isn't free ? I know that for free groups there is the Nielsen-Schreier ...
73 views

### finite generated monoid by two elements.

If $H$ be a monoid generated by two generators $h_1, h_2$ then H is a free monoid?
19 views

### semigroup in which Green's relations are different

I am beginning to study the Green relations and I would like to know if there is a semigroup in which the 5 Green relations are different. I would like to find an example where this occurs, I have ...
56 views

### Group actions on semigroups and groups

When a group acts on a set, many doors open up. The orbits partition the set, the stabilizers are subgroups, the kernel is a normal subgroup, the size of an orbit is the index of the stabilizer, the ...
69 views

### Good book for self-study of Magmas/Semigroups/etc.?

I'm currently an undergrad in my second semester of Abstract Algebra. We've covered groups, rings, fields, all that fun stuff. I'm working with Shahriari's "Algebra in Action" as well as ...
17 views

413 views

### Are all commutative, associative binary operations isomorphic to addition?

Addition and multiplication are the two classic commutative, associative binary operations on the reals. They satisfy a striking property: they are equivalent up to unary operations. By taking a ...
46 views

Suppose $X$ is a metric space, and let $X^*$ denote the free monoid on $X$, that is the monoid consisting of all finite strings of elements of $X$, with string concatenation as the monoid operation (...
59 views

### Why do we talk about $C_0$-semigroups and not $C_0$-monoids?

I see how for an alebraic structure to be a group then we'd kind of need an inverse element, which is unnecessary for the solutions of DEs. But an identity element is pretty important, isn't it? On ...
I've begun reading Steinberg's book on representations of finite monoids. In the very first chapter, he introduces congruences on a monoid as an equivalence relation $\equiv$ such that $x \equiv y$ ...