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Results tagged with semigroups-and-monoids
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user 290
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.
76
votes
Accepted
Why aren't representations of monoids studied so much?
Certainly irreducible representations exist; one can still construct the monoid algebra of a monoid and consider modules over the algebra. But Maschke's theorem is false in general for finite monoids …
- 118k
5
votes
Magma "actions" (or alternatively, "What is the Yoneda lemma for magmas?")
An action $S$ of a magma $M$ is a function $M \times S \to S$ satisfying no extra conditions. (If you imposed any conditions then $M$ wouldn't act on itself.) This lets you write down trees where some …
- 118k
4
votes
Wants: Polynomial Time Algorithm for Decomposing a Multiset of Rationals into Two Additive S...
Going off of fedja's comment I'll assume you want unique representations. In that case, one small observation is as follows: if $d$ is the least common denominator of the elements of $S$ and $S = \{ …
- 118k