degree

《Cohomologie Locale Des Faisceaux Coherents (Sga 2): Seminaire De Geometrie Algebrique Du Bois Marie 1962 (Documents Mathematiques)》 · 第 2 页 · Section 1.1「Definitions and Examples」的对象约定及次数定义（省略中间关于矩阵与复合顺序的约定）

Let $G$ denote a finite group, and let $R$ be a commutative ring with a $1$. If $V$ is an $R$-module, we denote it by $GL(V)$ the group of all invertible $R$-module homomorphisms $V\to V$. […] A (linear) representation of $G$ (over $R$) is a group homomorphism $\rho:G\to GL(V)$. In a situation where $V$ is free as an $R$-module, on taking a basis for $V$, we may write each element of $GL(V)$ as a matrix with entries in $R$, and we obtain for each $g\in G$ a matrix $\rho(g)$. These matrices multiply together in the manner of the group, and we have a matrix representation of $G$. In this situation, the rank of the free $R$-module $V$ is called the degree of the representation.