Let R be a 2-torsion free ring and L a Lie ideal of R. An additive mapping F:R®R is called a generalized derivation on R if there exists a derivation d:R®R such that F(xy)=F(x)y+xd(y) holds for all x, yÎR. In the present paper we describe the action of generalized derivations satisfying several conditions on Lie ideals of semiprime rings.

In this paper, we investigate the relationship between symmetric bi-semiderivations and Lie ideals of a prime ring. Additionally, we extend some well-known results concerning symmetric biderivations of prime rings to symmetric bi-semiderivations.

In this paper, we define the conceps of complex fuzzy Lie subalgebras and complex fuzzy ideals of Lie algebras with respect to t-norms and investigate some of characteristics and relationship between them. Next, we introduce the concepos of quotient subalgebras, intersection, sum and direct product of them and prove some results about them. Finally, we introduce and study the image and the inverse image of them under Lie algebra homomorphisms.

Let R be a prime ring with center Z(R) and G be a generalized α-derivation of R for α∈ Aut(R). Let a ∈ R be a nonzero element and n be a fixed positive integer. (i) If aG(x)n ∈ Z(R) for all x ∈ R then aG(x) = 0 for all x ∈ R unless dimCRC = 4. (ii) If aG(x)n ∈ Z(R) for all x ∈ L, where L is a noncommutative Lie ideal of R then aG(x) = 0 for all x ∈ R unless dimCRC = 4

Schur proved that if the center of a group G has finite index, then the derived subgroup G′ is also finite. Moneyhun proved that if L is a Lie algebra such that dim(L/Z(L)) = n, then dim(L^2) ≤1/2n(n-1) In this paper, we extend the converse of Moneyhun’s theorem. Also, we prove a wellknown result of nilpotent Lie algebras by using a different technique

In this paper, we study a generalization of z-ideals in the ring C (X) of continuous real valued functions on a completely regular Hausdorff space X. The notion of a weak ideal and naturally a weak z-ideal and a prime weak ideal are introduced and it turns out that they behave such as z -ideals in C (X).