Huang, S. (2015). Derivations with power values on multilinear polynomials. Iranian Journal of Science and Technology (Sciences), 39(4), 521-525. doi: 10.22099/ijsts.2015.3404

S. Huang. "Derivations with power values on multilinear polynomials". Iranian Journal of Science and Technology (Sciences), 39, 4, 2015, 521-525. doi: 10.22099/ijsts.2015.3404

Huang, S. (2015). 'Derivations with power values on multilinear polynomials', Iranian Journal of Science and Technology (Sciences), 39(4), pp. 521-525. doi: 10.22099/ijsts.2015.3404

Huang, S. Derivations with power values on multilinear polynomials. Iranian Journal of Science and Technology (Sciences), 2015; 39(4): 521-525. doi: 10.22099/ijsts.2015.3404

Derivations with power values on multilinear polynomials

^{}School of Mathematics and Finance, Chuzhou University, China

Abstract

A polynomial

1 2 ( , , , ) n f X X X
is called multilinear if it is homogeneous and linear in every one of its
variables. In the present paper our objective is to prove the following result: Let

R be a prime K-algebra over a
commutative ring

K with unity and let 1 2 ( , , , ) n f X X X be a multilinear polynomial over K. Suppose
that

d is a nonzero derivation on R such that 1 2 1 2 ( , , , ) ( , , , ) s t
df x x x

n f x x xn for all
1 2

, , , n x x x R, where s,t are fixed positive integers. Then 1 2 ( , , , ) n f X X X is central-valued on
R . We also examine the case R which is a semiprime K-algebra.