In this paper we introduce the concepts of higher {Lgn , Rhn }-derivation, higher {gn, hn}-derivation and Jordan higher {gn, hn}-derivation. Then we give a characterization of higher {Lgn , Rhn ...}-derivations and higher {gn, hn}-derivations in terms of {Lg, Rh}-derivations and {g, h}-derivations, respectively. Using this result, we prove that every Jordan higher {gn, hn}-derivation on a semiprime algebra is a higher {gn, hn}-derivation. In addition, we show that every Jordan higher {gn, hn}- derivation of the tensor product of a semiprime algebra and a commutative algebra is a higher {gn, hn}-derivation. Moreover, we show that there is a one to one correspondence between the set of all higher {Lgn , Rhn }-derivations and the set of all sequences of {LGn , RHn }-derivations. Also, it is presented that if A is a unital algebra and {fn} is a generalized higher derivation associated with a sequence {dn} of linear mappings, then {dn} is a higher derivation. Some other related results are also discussed.
Let A be a standard operator algebra on an infinite dimensional complex
Hilbert space H containing identity operator I, which is closed under the
adjoint operation. Suppose that ? : U ? U is the ...nonlinear mixed Jordan
triple *- derivation. Then ? is an additive *-derivation.
The present paper aims to study the connection between commutativity of rings and the behaviour of their generalized derivations. More precisely, we investigate the commutative prime rings
R
, which ...admit generalized derivations
Ψ
,
Φ
, and
Θ
satisfying specific differential identities on a certain subset of
R
.
Let R be any arbitrary associative ring and P be a prime ideal of R. In this article, we define and study the notion of P-derivation, generalized P-derivation and P-multiplier. We present theorems on ...the structure of the factor ring R/P and the description of these mappings in some specific situations.
According to Posner’s second theorem, a prime ring is forced to be commutative if a nonzero centralizing derivation exists on it. In this article, we extend this result to prime rings with ...antiautomorphisms and nonzero skew derivations. Additionally, a case is shown to demonstrate that the restrictions placed on the theorems’ hypothesis were not unnecessary.
We define an R-linear map φ from A to an A-bimodule M is said to be Jordan homo-derivation if φ(x2) = φ(x)x + xφ(x) + φ(x)2 for each x ∈ A. In this article, we proved that every Jordan ...homo-derivation to be homo-derivation on triangular algebras.
Let
be a unital *-algebra containing a non-trivial projection. In this paper, it is shown that a map Γ:
such that
for all
. Then Γ is an additive *-derivation.
Let
be a power of prime
. In this article, we investigate the reversible cyclic codes of arbitrary length
over the ring
= 𝔽
+
+
, where
= 0 mod
. Further, we find a unique set of generators for ...cyclic codes over
and classify the reversible cyclic codes with their generators. Moreover, it is shown that the dual of reversible cyclic code over
is reversible. Finally, some examples of reversible cyclic codes are provided to justify the importance of these results.
Let R be a prime ring of characteristic different from 2, Q
r
its right Martindale quotient ring, L a non-central Lie ideal of R (i.e.,
),
a fixed integer, F and G two generalized skew derivations of ...R, associated with the same automorphism α of R. If
, for any
, then there exists
such that
, for any
, unless when R satisfies the standard polynomial identity
.
This paper's primary goal is to look at a quotient ring $\mathscr{A}/\mathscr{T}$ structure, where $\mathscr{A}$ is an arbitrary ring and $\mathscr{T}$ is a semi-prime ideal of $\mathscr{A}$. More ...precisely, we examine the differential identities in a semi-prime ideal of an arbitrary ring involving $\mathscr{T}$-commuting generalized derivation. Furthermore, examples are given to prove that the restrictions imposed on the hypothesisof the various theorems were not superfluous.
