##  [Monomial Order](/monomial-order) 

  ##  [Monomial Order](https://algebra.quantumdictionary.io/monomial-order-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A total well-ordering on the set of monomials of a polynomial ring that is compatible with multiplication (if u < v then uw < vw for every monomial w); monomial orders determine leading terms and are essential to polynomial reduction and Gröbner-basis theory.