Let R be a ring and let g be an endomorphism of R. The additive mapping d: R -> R is called a Jordan semiderivation of R, associated with g, if d(x(2)) = d(x)x + g(x)d(x) = d(x)g(x) + xd(x) and d(g(x)) = g(d(x)) for all x is an element of R. The additive mapping F: R -> R is called a generalized Jordan semiderivation of R, related to the Jordan semiderivation d and endomorphism g, if F(x(2)) = F(x)x + g(x)d(x) = F(x)g(x) + xd(x) and F(g(x)) = g(F(x)) for all x is an element of R. In this paper we prove that if R is a prime ring of characteristic different from 2, g an endomorphism of R, d a Jordan semiderivation associated with g, F a generalized Jordan semiderivation associated with d and g, then F is a generalized semiderivation of R and d is a semiderivation of R. Moreover, if R is commutative, then F = d.

### Generalized Jordan Semiderivations in Prime Rings

#### Abstract

Let R be a ring and let g be an endomorphism of R. The additive mapping d: R -> R is called a Jordan semiderivation of R, associated with g, if d(x(2)) = d(x)x + g(x)d(x) = d(x)g(x) + xd(x) and d(g(x)) = g(d(x)) for all x is an element of R. The additive mapping F: R -> R is called a generalized Jordan semiderivation of R, related to the Jordan semiderivation d and endomorphism g, if F(x(2)) = F(x)x + g(x)d(x) = F(x)g(x) + xd(x) and F(g(x)) = g(F(x)) for all x is an element of R. In this paper we prove that if R is a prime ring of characteristic different from 2, g an endomorphism of R, d a Jordan semiderivation associated with g, F a generalized Jordan semiderivation associated with d and g, then F is a generalized semiderivation of R and d is a semiderivation of R. Moreover, if R is commutative, then F = d.
##### Scheda breve Scheda completa Scheda completa (DC)
2015
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/11570/3060477
##### Attenzione

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

• ND
• 11
• 11