From Humphreys' Introduction to Lie Algebras and Representation Theory:

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> Let $\text{End }V$ denote the set of linear transformations $V\rightarrow V$, and we write $\mathfrak{gl}(V)$ for $\text{End }V$ viewed as Lie algebra. We write down the multiplicatio ntable for $\mathfrak{gl}(n,F)$ relative to the standard basis consisting of the matrices $e\_{ij}$ (having $1$ in the $(i,j)$ position and $0$ elsewhere). Since $[e\_{ij},e\_{kl}]=\delta\_{jk}e\_{il}-\delta\_{li}e\_{kj}$, it follows that $[e\_{ij},e\_{kl}]=\delta\_{jk}e\_{il}-\delta\_{li}e\_{kj}$. Notice that the coefficients are all $\pm 1$ or $0$; in particular, all of them lie in the prime field of $F$.
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What does it mean to lie in the prime field of $F$? A prime field $GF(p)$ is the field of residue classes modulo $p$. How does it have anything to do with matrices with coefficients $-1,0,1$?