Editing Emmy Noether (section)

====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 [[polynomial factorization|factorization of polynomials]] could be carried over directly.{{sfn|Noether|1923}}{{sfn|Noether|1923b}}{{sfn|Noether|1924}} 

Traditionally, elimination theory is concerned with eliminating one or more variables from a system of polynomial equations, often by the method of [[resultant]]s.{{sfn|Cox|Little|O'Shea|2015|p=121}}
For illustration, a system of equations often can be written in the form
: {{math|1= Mv = 0 }}
where a matrix (or [[linear transform]]) {{math|M}} (without the variable {{math|x}}) times a vector {{math|v}} (that only has non-zero powers of {{math|x}}) is equal to the zero vector, {{math|0}}. Hence, the [[determinant]] of the matrix {{math|M}} must be zero, providing a new equation in which the variable {{math|x}} has been eliminated.