Commutative Algebra with a View Toward Algebraic Geometry
《Commutative Algebra with a View Toward Algebraic Geometry》 · 第 42 页 · Chapter 1「Roots of Commutative Algebra」
Let $M$ be a finitely generated graded module over $k[x_1,\ldots,x_r]$, with grading by degree. The numerical function $H_M(s):=\dim_k M_s$ is called the Hilbert function of $M$.