Functional identities of degree 2 in triangular rings

Functional identities of degree 2 in CSL algebras

‎Let $mathscr{L}$ be a commutative subspace lattice generated by finite many commuting independent nests on a complex separable Hilbert space $mathbf{H}$ with ${rm dim}hspace{2pt}mathbf{H}geq 3$‎, ‎${rm Alg}mathscr{L}$‎ ‎the CSL algebra associated with $mathscr{L}$ and $mathscr{M}$ be an algebra containing ${rm Alg}mathscr{L}$‎. ‎This article is aimed at describing the form of‎ ‎additive mapppi...

Differential Polynomial Rings of Triangular Matrix Rings

On Identities with Additive Mappings in Rings

begin{abstract} If $F,D:Rto R$ are additive mappings which satisfy $F(x^{n}y^{n})=x^nF(y^{n})+y^nD(x^{n})$ for all $x,yin R$. Then, $F$ is a generalized left derivation with associated Jordan left derivation $D$ on $R$. Similar type of result has been done for the other identity forcing to generalized derivation and at last an example has given in support of the theorems. end{abstract}

Left Annihilator of Identities Involving Generalized Derivations in Prime Rings

Let $R$ be a prime ring with its Utumi ring of quotients $U$,  $C=Z(U)$ the extended centroid of $R$, $L$ a non-central Lie ideal of $R$ and $0neq a in R$. If $R$ admits a generalized derivation $F$ such that $a(F(u^2)pm F(u)^{2})=0$ for all $u in L$, then one of the following holds: begin{enumerate} item there exists $b in U$ such that $F(x)=bx$ for all $x in R$, with $ab=0$; item $F(x)=...

differential polynomial rings of triangular matrix rings