I have found in some sources that the ring $R=\mathbb{F}_p[x_1,\dots,x_n]/(x_1^p,\dots,x_n^p)$ is a local complete intersection ring.
I need this result in order to apply a related theorem and I would like to understand why this is true. I see why $R$ is local, artinian and injectif. However, for the complete intersection propriety, I don't really understand neither what does it mean.
Clearly we have:
$$\frac{\mathbb{F}_p[x_1,\dots,x_n]}{(x_1^p,\dots,x_n^p)}\simeq \frac{\mathbb{F}_p[x_1]}{(x_1^p)}\otimes\dots\otimes\frac{\mathbb{F}_p[x_n]}{(x_n^p)} $$ so I suppose that proving just $\mathbb{F}_p[x_1]/(x_1^p)$ is a complete intersection ring it is enough and an easier task, but I don't know how to procede anymore.