A ONE-SIDED VERSION OF POSNERS SECOND THEOREM ON MULTILINEAR POLYNOMIALS

Title & Authors
A ONE-SIDED VERSION OF POSNERS SECOND THEOREM ON MULTILINEAR POLYNOMIALS
FILIPPIS VINCENZO DE;

Abstract
Let K be a commutative ring with unity, R a prime K-algebra of characteristic different from 2, d a non-zero derivation of R, I a non-zero right ideal of R, f($\small{x_1,{\cdots},\;x_n}$) a multilinear polynomial in n non-commuting variables over K, a $\small{\in}$ R. Supppose that, for any $\small{x_1,{\cdots},\;x_n\;\in\;I,\;a[d(f(x_1,{\cdots},\;x_n)),\;f(x_1,{\cdots},\;x_n)]}$
Keywords
prime rings;derivations;generalized polynomial identities;
Language
English
Cited by
References
1.
K. I. Beidar, W. S. Martindale III, and V. Mikhalev, Rings with generalized identities, Pure and Applied Math., Dekker, New York, 1996

2.
C. L. Chuang, GPIs having coefficients in Utumi quotient rings, Proc. Amer. Math. Soc. 103 (1988), 723-728

3.
C. M. Chang and T. K. Lee, Additive subgroup generated by polynomial values on right ideals, Comm. Algebra 29 (2001), no. 7, 2977-2984

4.
V. De Filippis and O. M. Di Vincenzo, Posner's second theorem and an annihilator condition, Math. Pannon. 12 (2001), no. 1, 69-81

5.
V. K. Kharchenko, Differential identities of prime rings, Algebra Logic 17 (1978), 154-168

6.
T. K. Lee, Derivations with Engel conditions on polynomials, Algebra Colloq. 5 (1998), no. 1, 13-24

7.
T. K. Lee, Semiprime rings with differential identities, Bull. Inst. Math. Acad. Sinica 20 (1992), 27-38

8.
U. Leron, Nil and power-central polynomials in rings, Trans. Amer. Math. Soc. 202 (1975), 97-103

9.
W. S. Martindale III, Prime rings satisfying a generalized polynomial identity, J. Algebra 12 (1969), 576-584

10.
L. Rowen, Polynomial identities in ring theory, Pure and Applied Math. vol. 84, Academic Press, New York, 1980

11.
T. L. Wong, Derivations with power-central values on multilinear polynomials, Algebra Colloq. 4 (1996), no. 3, 369-378