Maps preserving zeros of a polynomial
  Let $\A$ be an algebra and let $f(x_1,...,x_d)$ be a multilinear polynomial in noncommuting indeterminates $x_i$. We consider the problem of describing linear maps $\phi:\A\to \A$ that preserve zeros of $f$. Under certain technical restrictions we solve the problem for general polynomials $f$ in the case where $\A=M_n(F)$. We also consider quite general algebras $\A$, but only for specific polynomials $f$. 
J. Alaminos, M. Bre\v{s}ar, \v{S}. \v{S}penko, A. R. Villena
math.RA math.RT