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Results tagged with semigroups-and-monoids
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user 62321
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.
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Question about actions of full transformation monoids
[Reposted from math.stackexchange]
Consider a monoid $M$ acting on a set $X$, where $M$ is the full transformation monoid on some set $A$ (i.e., the set of all functions from $A$ to itself, with func …
- 167
2
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Accepted
Question about actions of full transformation monoids
The answer to Question 2 is also "yes". Trivially so if $B\subseteq B'$ or $B'\subseteq B$, so assume otherwise. Given the affirmative answer to Question 1, it suffices to show that $mx=x$ when $mb=b$ …
- 167