An analogue of the Erdős-Ginzburg-Ziv theorem for quadratic symmetric polynomials.
We prove that every locally nilpotent monomial k-derivation of k[X₁,...,Xₙ] is triangular, whenever k is a ring of characteristic zero. A method of testing monomial k-derivations for local nilpotency is also presented.
Let be a finite commutative ring with unity. We determine the set of all possible cycle lengths in the ring of polynomials with rational integral coefficients.