PROMOTING ACCESS TO AFRICAN RESEARCH

Quaestiones Mathematicae

Log in or Register to get access to full text downloads.

Remember me or Register



DOWNLOAD FULL TEXT Open Access  DOWNLOAD FULL TEXT Subscription or Fee Access

Strong commutativity preserving generalized derivations on multilinear polynomials

Nurcan Argaç, Giovanni Scudo

Abstract


Let R be a non-commutative prime ring of characteristic different from 2, with right Utumi quotient ring U and extended centroid C  and let F and G be generalized derivations of R such that F(x)G(y)-F(y)G(x) = [x; y], for all x; y ∈ S, where S is a subset of R. Here we will discuss the following cases:

(a) S = [R;R];

b) S = L, where L is a non-central Lie ideal of R;

(c) S = ƒ(R), where ƒ(R) is the set of all evaluations of a non-central multilinear polynomial ƒ(x1; : : : ; xn) on R.

In all cases, if R does not satisfy s4(x1; : : : ; x4), the standard polynomial identity on 4 non-commuting variables, then there exist s; c ∈ U such that F(x) = xs, G(x) = cx, for all x ∈ R, and sc = 1C (the unit of C). We also study the semiprime case.


Mathematics Subject Classification (2010): 16W25, 16N60.
Key words: Prime rings, differential identities, generalized derivations.




http://dx.doi.org/10.2989/16073606.2017.1348398
AJOL African Journals Online