section_path: Contributions to mathematics and physics/Second epoch (1920–1926)/Elimination theory
section_name: Elimination theory
paragraph_text: Elimination theory
  
  In 1923–1924, Noether applied her ideal theory to elimination theory in a formulation that she attributed to her student, Kurt Hentzelt. She showed that fundamental theorems about the factorization of polynomials could be carried over directly. Traditionally, elimination theory is concerned with eliminating one or more variables from a system of polynomial equations, usually by the method of resultants.
  
  For illustration, a system of equations often can be written in the form
  
  where a matrix (or linear transform) M (without the variable x) times a vector v (that only has non-zero powers of x) is equal to the zero vector, 0. Hence, the determinant of the matrix M must be zero, providing a new equation in which the variable x has been eliminated.