Use this tag for questions related to ideals generated by binomials.
Consider $\mathbb K[\mathbf x]$ with $\mathbb K^\ast = \mathbb K \setminus \{ 0\}.$ We typically assume that $\mathbb K$ is algebraically closed so that $\mathbb K = \mathbb C$ is our default coefficient field. Then $$I = \langle c_{\mathbf a} x^{\mathbf a} − c_{\mathbf b} x^{\mathbf b} | \mathbf a, \mathbf b \in \mathbb N^n, c_{\mathbf a}, c_{\mathbf b} ∈ \mathbb K^\ast \rangle$$ is a binomial ideal.
For more information, see the lecture notes "Binomial Ideals" or "Expanded lectures on binomial ideals."