Garside element

In mathematics, a Garside element is an element of an algebraic structure such as a monoid that has several desirable properties. 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.

Garside element

In mathematics, a Garside element is an element of an algebraic structure such as a monoid that has several desirable properties. 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.