Let A and B be two (complex) algebras. A linear map φ: A → B is called an n-homomorphism if φ(a1 . . . an) =φ(a1) . . .φ(an) for each a1, . . . , an Є A. In this paper, we investigate n-homomorphisms and their relation to homomorphisms. We characterize n-homomorphisms in terms of homomorphisms under certain conditions. Some results related to continuity and commutativity is given as well.  

This article presents an interaction between functional homomorphisms, dynamical systems and differential equations. The exponential functions play pivotal role in this interaction.

‎In this paper‎, ‎we introduce a class of higher homomorphisms on an algebra $ \mathcal{A} $ and we characterize the structure of them as a linear combination of some ‎sequences‎ of homomorphisms‎.‎ ‎Also ‎‎we prove that for any approximate higher ring homomorphism on a Banach algebra $ \mathcal{A} $ under some sequences of control funtions‎, there exists a unique higher ring homomorphism near it. Using special sequences of control functions, we show that the approximate higher ring homomorphism is an exact higher ring homomorphism.

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

Using  xed point method, we prove some new stability results for Lie ( ;  ; )-derivations and Lie C-algebra homomorphisms on Lie C-algebras associated with the Euler-Lagrange type additive functional equation....