ANNIHILATOR CONDITIONS OF DERIVATIONS ON MULTILINEAR POLYNOMIALS

作者：Wang, Yu^*

来源：Communications in Algebra, 2011, 39(1): 237-246.

DOI：10.1080/00927870903337992

• Derivations
• Multilinear polynomials
• Prime rings
• Right ideals

Let R be a prime ring with extended centroid C and two-sided Martindale quotient ring Q. Let d be a nonzero derivation of R, f(x(1), ..., x(n)) a multilinear polynomial over C, b is an element of R, and I a nonzero right ideal of R. Suppose that
b[d(f(r(1), ..., r(n))), f(r(1), ..., r(n))](k) = 0
for all r(i) is an element of I. If bI = 0, then either bd(I) = 0 or there exists an idempotent element e is an element of soc(RC) such that IC = eRC and f(x(1), ..., x(n)) is a PI for eRCe. If bI not equal 0, then there exists an idempotent element e is an element of soc(RC) such that IC = eRC and one of the following holds:
(i) d = ad(a) for some a is an element of Q such that aI = 0 and f(x(1), ..., x(n))(k+1) is central-valued on eRCe;
(ii) f(x(1), ...

• 出版日期2011
• 单位上海师范大学