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Results tagged with semigroups-and-monoids
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user 4600
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.
7
votes
1
answer
441
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Which monoids have a faithful irreducible representation?
Let $*$ be a binary operation on a set $M$, with an identity element $e\in M$.
A monoid representation of $(M,*,e)$ is a map $\delta:M\to (S\to S)$ for some set $S$, such that $\delta(e)=\mathrm{id}_S …
- 24.8k
9
votes
Accepted
Is the equational theory of groups axiomatized by the associative law?
Yes. It suffices to show that any free semigroup embeds in a group.
For this I refer you to MO question 3235:
Let $F$ be a free semigroup (say, $2$-generated) which is embedded in a group $G$, an …
- 24.8k
8
votes
Accepted
Define Turing machine with algebraic concepts/structures
Yes, there is now Pavlovic's characterization of Turing computability in terms of the monoidal computer, based on monoidal categories. http://arxiv.org/abs/1208.5205
- 24.8k
7
votes
Accepted
Über theorem on unavoidable patterns?
According to the 2013 paper "Computing the Partial Word Avoidability Indices of
Ternary Patterns" by Blanchet-Sadri, Lohr, and Scott,
The problem of deciding whether a given pattern is avoidable h …
- 24.8k