Introduction to Mathematical Logic, Sixth Edition
《Introduction to Mathematical Logic, Sixth Edition》 · 印刷第 226—227 页 Section 5.1「Polynomial Invariants for Reductive Groups」，不变多项式的条件、Theorem 5.1.1 完整陈述与 Definition 5.1.2
For an algebraic group $G$ acting by a regular representation on a vector space $V$, the ring of invariants is the algebra of polynomial functions $f$ on $V$ such that $f(gv)=f(v)$ for all $v\in V$ and $g\in G$. […] Theorem 5.1.1. Suppose $G$ is a reductive linear algebraic group acting by a regular representation on a vector space $V$. Then the algebra $\mathcal P(V)^G$ of $G$-invariant polynomials on $V$ is finitely generated as a $\mathbb C$-algebra. […] Definition 5.1.2. Let $\{f_1,\ldots,f_n\}$ be a set of generators for $\mathcal P(V)^G$ with $n$ as small as possible. Then $\{f_1,\ldots,f_n\}$ is called a set of basic invariants.