an element, x, of a ring, R, is called nilpotent if there exists some positive integer, n, such that $x^n = 0$.
in book Skew Fields by P.K. DRAXL : Definition 3 . A simple ring $A$ with finite $|A:Z(A)|$ is called a "central simple $K-algebra$" ($ K := Z(A)$ ). If a central simple $ K$-algebra is a skew field then we call it a "$K$-skew field".
now is following statement true ?
let every $D_{i}$ is $K$-skew field then $ \otimes _{i=1}^{n} D_{i}$ is nilpotent iff every $D_{i}$ is nilpotent .($ \otimes $ : is tensor product over $K$. we say that $D_{i}$ is nilpotent if $D_{i}$ has maximal subfield $F$ and $F/Z(D_i)$ Galois extension and Galois group $Gal(F/Z(D_i))$ be nilpotent group)
I think it is not true but i can't find counterexample.