Let R be a prime ring, f(x(1),...,x(n)) a multilinear polynomial over C in n noncommuting indeterminates, I a nonzero right ideal of R, and F : R -> R be a nonzero generalized skew derivation of R. Suppose that F(f(r(1),...,r(n)))f(r(1),...,r(n)) is an element of C, for all r(1),...,r(n) is an element of I. If f(x(1),...,x(n)) is not central valued on R, then either char(R) = 2 and R satisfies s(4) or one of the following holds: (i) f (x(1),...,x(n))x(n+1) is an identity for I; (ii) F(I)I = (0); (iii) [f(x(1),...,x(n)),x(n+1)]x(n+2) is an identity for I, there exist b,c,q is an element of Q with q an invertible element such that F(x) = bx - qxq(-1) c for all x is an element of R, and q(-1)cI subset of I. Moreover, in this case either (b - c)I = (0) or b c is an element of C and f(x(1),...,x(n))(2) is central valued on R.

### Generalized Skew Derivations On Multilinear Polynomials In Right Ideals of Prime Rings

#### Abstract

Let R be a prime ring, f(x(1),...,x(n)) a multilinear polynomial over C in n noncommuting indeterminates, I a nonzero right ideal of R, and F : R -> R be a nonzero generalized skew derivation of R. Suppose that F(f(r(1),...,r(n)))f(r(1),...,r(n)) is an element of C, for all r(1),...,r(n) is an element of I. If f(x(1),...,x(n)) is not central valued on R, then either char(R) = 2 and R satisfies s(4) or one of the following holds: (i) f (x(1),...,x(n))x(n+1) is an identity for I; (ii) F(I)I = (0); (iii) [f(x(1),...,x(n)),x(n+1)]x(n+2) is an identity for I, there exist b,c,q is an element of Q with q an invertible element such that F(x) = bx - qxq(-1) c for all x is an element of R, and q(-1)cI subset of I. Moreover, in this case either (b - c)I = (0) or b c is an element of C and f(x(1),...,x(n))(2) is central valued on R.
##### Scheda breve Scheda completa Scheda completa (DC)
2014
File in questo prodotto:
Non ci sono file associati a questo prodotto.
##### Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11570/2742769`
##### Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

##### Citazioni
• ND
• 5
• 4