1998/01/01 by Mark L. Green · 3 citations
Computer Science · Mathematics · #Algebra over a field #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Commutative algebra #Commutative property #Computer science #Epistemology #Ideal (ethics) #Mathematics #Object (grammar) #Philosophy #Polynomial and algebraic computation #Pure mathematics
paper · doi:10.1007/978-3-0346-0329-4_2
openalex publication_date 1998/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
A very powerful technique in commutative algebra was introduced by Macaulay, who realized that studying the initial terms of elements of an ideal gives one great insight into the algebra and combinatorics of the ideal. The initial ideal depends on the choice of coordinates, but there is an object, the initial ideal in generic coordinates, which is coordinate-independent. Generic initial ideals appeared in the work of Grauert and Hironaka. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.