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Results tagged with semigroups-and-monoids
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user 120914
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.
3
votes
examples of finitely generated semigroups that are not residually finite
To generalise @BenjaminSteinberg's (by now rather old) answer, Lallement showed in 1971 that a one-relation monoid $M = \text{Mon}\langle A \mid w= w'\rangle$ where $w$ is a left and right factor of $ …
17
votes
Are all free monoids residually finite?
The standard meaning of residually finite here is that for every pair of elements $u, v$ in the free monoid $A^\ast$, if $u \neq v$ then there is a homomorphism $\phi \colon A^\ast \to F$ with $F$ a f …
3
votes
What's the current state of one-rule semi-Thue system termination problem?
An important part of this problem is, as Ben points out in his answer, the word problem for one-relation monoids. This problem is still open, but it has been reduced to a number of special cases. I'll …