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Results tagged with semigroups-and-monoids
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user 157261
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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Can every cancellative invertible-free monoid be embedded in a group?
No, it is not true even for finitely generated monoids. Take any semigroup $S$ which is cancellative and does not embed into a group (first examples were constructed by Malcev). Consider the monoid $S …
- 1,832
2
votes
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More vocabulary for periodic elements in monoids
Question 1: See Clifford and Preston, volume 1.
Question 2: $m$ is the period, $n$ is called the index of the element. See this Wikipedia text.
Question 3: If $n=1$, the element is called a group elem …
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