Garside_element
Garside element
Element of algebraic structure
In mathematics, a Garside element is an element of an algebraic structure such as a monoid that has several desirable properties.
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Formally, if M is a monoid, then an element Δ of M is said to be a Garside element if the set of all right divisors of Δ,
is the same set as the set of all left divisors of Δ,
and this set generates M.
A Garside element is in general not unique: any power of a Garside element is again a Garside element.