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Results tagged with semigroups-and-monoids
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user 10605
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.
19
votes
Accepted
Semi group of polynomials which all roots lie on the unit circle
A complex polynomial is uniquely determined by its set of roots together with multiplicities. This means that the semigroup of your polynomials is freely generated by the set of point on the unit circ …
- 4,780
9
votes
2
answers
1k
views
Ternary associative multiplication
In this answer Brian M. Scott describes the following generalization of a binary associative multiplication to a ternary one: it is a function $$[\cdot,\cdot,\cdot] : G\times G \times G \to G$$ such t …
- 4,780