semigroup - crowlogic/arb4j GitHub Wiki
A semigroup
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Closure: For all
$a, b$ in$S$ , the result of the operation, or product,$a * b$ , is also in$S$ .
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Associativity: For all
$a, b$ and$c$ in$S$ , the equation$(a * b) * c = a * (b * c)$ holds.
Note that a semigroup does not require the presence of an identity element, nor the existence of inverses, unlike groups. Thus, a semigroup can be thought of as a group without the requirements of having an identity and being invertible.