# What is a “p-linear endomorphism”?

I came across this terminology but don't know what it means: "p-linear endomorphism".

More specifically, it said "Let F be a p-linear endomorphism of a vector space V".

Can someone explain it to me?

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Can you give more context? – Davide Giraudo Apr 22 '12 at 16:26

In some papers, $p$-linear just means... homogeneous of degree $p$. More precisely, it seems that this terminology is used when working on structures with finite characteristic. I've read that an andomorphism $F$ is $1/p$-linear when $F(\alpha x)=\alpha^{\frac{1}{p}}F(x)$ for each $x$ and $\alpha$.
I have never seen $p$-linear used this way, do you have references to papers where this is done? – Gunnar Þór Magnússon Apr 22 '12 at 16:48