In the present paper we study generalized left derivations on Lie ideals of rings with involution. Some of our results extend other ones proven previously just for the action of generalized left derivations on the whole ring. Furthermore, we prove that every generalized Jordan left derivation on a 2-torsion free ∗-prime ring with involution is a generalized left derivation.

Proof theoretic characterizations of complexity classes are of considerable interest because they link levels of conceptual abstraction to computational complexity. We consider here the provability of functions over coinductive data in a highly expressive, yet proof-theoretically weak, variant of second order logic L ∗ , which we believe captures the notion of feasibility more broadly than prev...

Let N be a near ring. An additive mapping f : N → N is said to be a right generalized (resp., left generalized) derivation with associated derivation d onN if f(xy) = f(x)y + xd(y) (resp., f(xy) = d(x)y + xf(y)) for all x, y ∈ N. A mapping f : N → N is said to be a generalized derivation with associated derivation d onN iff is both a right generalized and a left generalized derivation with asso...

We introduce the concepts of memory-hard algorithms and sequential memory-hard functions, and argue that in order for key derivation functions to be maximally secure against attacks using custom hardware, they should be constructed from sequential memory-hard functions. We present a family of key derivation functions which, under the random oracle model of cryptographic hash functions, are prov...

Let R be a prime ring, H a generalized derivation of R and L a noncommutative Lie ideal of R. Suppose that usH(u)ut = 0 for all u ∈ L, where s ≥ 0, t ≥ 0 are fixed integers. Then H(x) = 0 for all x ∈ R unless char R = 2 and R satisfies S4, the standard identity in four variables. Let R be an associative ring with center Z(R). For x, y ∈ R, the commutator xy− yx will be denoted by [x, y]. An add...

Let $ {\mathcal{A}} be a unital \ast -algebra containing nontrivial projection. Under some mild conditions on , it is shown that map \Phi:{\mathcal{A}}\rightarrow{\mathcal{A}} nonlinear mixed Jordan triple * -derivation if and only \Phi an additive -derivation. In particular, we apply the above result to prime -algebras, von Neumann algebras with no central summands of type I_{1} factor algebra...

We define, for each subset $S$ of the set $\mathcal{P}$ primes, an $S_n$-module $Lie_n^S$ with interesting properties. $Lie_n^\emptyset$ is well-known representation $Lie_n$ $S_n$ afforded by free Lie algebra, while $Lie_n^\mathcal{P}$ module $C\!onj_n$ conjugacy action on $n$-cycles. For arbitrary $Lie_n^{S}$ interpolates between representations and $C\!onj_n.$ consider symmetric exterior powe...

Let A be a prime *-algebra. In this paper, we suppose that ? : satisfies ?(A B) = ?(A) B + ?(B) where A*B B*A for all A, A. Then, is an additive *-derivation.