A Quadripartitioned Neutrosophic Pythagorean (QNP) set is a powerful general format framework that generalizes the concept of Quadripartitioned Neutrosophic Sets and Neutrosophic Pythagorean Sets. In ...this paper, we apply the notion of quadripartitioned Neutrosophic Pythagorean sets to Lie algebras. We develop the concept of QNP Lie subalgebras and QNP Lie ideals. We describe some interesting results of QNP Lie ideals.
Let R be a prime ring of characteristic not 2 and U be a noncentral square closed Lie ideal of R. An additive mapping Hon R is called a homoderivation if H(xy) =H(x)H(y)+H(x)y+xH(y)for all x, y∈R. In ...this paper we investigate homoderivations satisfying certain differential identitieson square closed Lie ideals of prime rings.
Let R be a prime ring of characteristic not 2 and U be a noncentral square closed Lie ideal of R. An additive mapping H on R is called a homoderivation if H(xy) = H(x)H(y)+H (x) y+xH(y) for all x, y ...∈ R. In this paper we investigate homoderivations satisfying certain differential identities on square closed Lie ideals of prime rings.
Let R be a prime ring of characteristic not 2 and U be a noncentral square closed Lie ideal of R. An additive mapping H on R is called a homoderivation if H(xy) = H(x)H(y)+H (x) y+xH(y) for all x, y ∈ R. In this paper we investigate homoderivations satisfying certain differential identities on square closed Lie ideals of prime rings.
Let R be a prime ring of characteristic not 2, L a nonzero square closed Lie ideal of R and let F : R → R, G : R → R be generalized derivations associated with derivations d : R → R, g : R → R ...respectively. In this paper, we study several conditions that imply that the Lie ideal is central. Moreover, it is shown that the assumption of primeness of R can not be removed.
Let A be an algebra and let f be a nonconstant noncommutative polynomial. In the first part of the paper, we consider the relationship between A,A, the linear span of commutators in A, and spanf(A), ...the linear span of the image of f in A. In particular, we show that A,A=A implies spanf(A)=A. In the second part, we establish some Waring type results for images of polynomials. For example, we show that if C is a commutative unital algebra over a field F of characteristic 0, A is the matrix algebra Mn(C), and the polynomial f is neither an identity nor a central polynomial of Mn(F), then every commutator in A can be written as a difference of two elements, each of which is a sum of 7788 elements from f(A) (if C=F is an algebraically closed field, then 4 elements suffice). Similar results are obtained for some other algebras, in particular for the algebra B(H) of all bounded linear operators on a Hilbert space H.
Let R be a prime ring with characteristic not 2 and σ,τ,λ,μ,α,β automorphisms of R. Let h be a nonzero left (resp. right)-generalized (σ,τ)-derivation of R and I,J nonzero ideals of R and a∈R. The ...main object in this article is to study the situations. (1) h(I)a⊂C_{λ,μ}(J) and ah(I)⊂C_{λ,μ}(J),(2) h(I)⊂C_{λ,μ}(J),(3) h(I),a_{λ,μ}=0, (4) h(I,a)_{λ,μ}=0 ( or (h(I),a)_{λ,μ}=0), (5) h(x),x_{λ,τ}=0,∀x∈I, (6) h(x)a,x_{λ,τ}=0,∀x∈I.
In this paper, basic concepts of soft set theory was mentioned. Then, bipolar soft Lie algebra and bipolar soft Lie ideal were defined with the help of soft sets. Some algebraic properties of the new ...concepts were investigated. The relationship between the two structures were analyzed. Also, it was proved that the level cuts of a bipolar soft Lie algebra were Lie subalgebras of a Lie algebra by the new definitions. After then, soft image and soft preimage of a bipolar soft Lie algebra/ideal were proved to be a bipolar soft Lie algebra/ideal.
Let A be a unital algebra over a field of characteristic different from 2. The main goal of this work is to characterize higher commutators of A. In particular, we show that if H is a noncommutative ...higher commutator of A and contains the unity, then H is equal to either A or A,A. As a result, we prove that if there exist x,y∈A such that 1=x,y, then the only higher commutators of A are A and A,A. We also consider the structure of noncommutative Lie ideals of the form U,A, where U is a Lie ideal of A, and show that if L=U,A is noncommutative and contains the unity, then L=A,A and A,A⊆U.
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