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Results tagged with semigroups-and-monoids
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user 126667
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.
28
votes
Accepted
Computing the structure of the group completion of an abelian monoid, how hard can it be?
Do people have good examples where it's "easy" to compute the group-completion of a commutative monoid, but for which the monoid itself is still rather mysterious?
This happens all the time in K- …
- 25.2k
13
votes
Is the semigroup M(n, Z) finitely presented? If so, where can I find a presentation of it?
Assuming by M(n, Z) you mean the semigroup (monoid) of n × n matrices over the integers under multiplication: no, it is not even finitely generated, because the determinant M(n, Z) → Z is multiplicati …
- 25.2k
5
votes
Homological algebra for commutative monoids?
I agree with Charles and Eric that the natural setting for your question is the model category of simplicial commutative monoids. However, my earlier guess that the resulting homotopy theory would ad …
- 25.2k
3
votes
References/literature for pushouts in category of commutative monoids? [ed. - amalgams]
I'm not sure exactly what you're looking for, but here is a somewhat weird example of a pushout in commutative monoids I recently came across:
$\begin{matrix}
\mathbb{N}&\to&\mathbb{Z}\\\\
\downarrow …
- 25.2k