Let R be a prime ring of characteristic different from 2, Z(R) its center, L a Lie ideal of R, and m, n, s, t ≥ 1 fixed integers with t ≤ m + n + s. Suppose that α is a non-trivial automorphism of R and let φ(x, y) = [x, y] t -[x, y] m [α([x, y]),[x, y]]n [x, y] s . Thus, (a) if φ(u, v) = 0 for any u, v L, then L ⊂ Z(R); (b) if φ(u, v) Z(R) for any u, v L, then either L ⊂ Z(R) or R satisfies s 4 , the standard identity of degree 4. We also extend the results to semiprime rings. © 2019 Academy of Mathematics and Systems Science, Chinese Academy of Sciences.

On certain identities with automorphisms on lie ideals in prime and semiprime rings

De Filippis;
2019-01-01

Abstract

Let R be a prime ring of characteristic different from 2, Z(R) its center, L a Lie ideal of R, and m, n, s, t ≥ 1 fixed integers with t ≤ m + n + s. Suppose that α is a non-trivial automorphism of R and let φ(x, y) = [x, y] t -[x, y] m [α([x, y]),[x, y]]n [x, y] s . Thus, (a) if φ(u, v) = 0 for any u, v L, then L ⊂ Z(R); (b) if φ(u, v) Z(R) for any u, v L, then either L ⊂ Z(R) or R satisfies s 4 , the standard identity of degree 4. We also extend the results to semiprime rings. © 2019 Academy of Mathematics and Systems Science, Chinese Academy of Sciences.
2019
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/11570/3150098
 Attenzione

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

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 0
social impact