Mustafa Asci

Some Properties of the

Riordan arrays are useful for solving the combinatorial sums by the help of generating functions. Many theorems can be easily proved by Riordan arrays. In this paper we consider the Pascal matrix and define a new generalization of Fibonacci polynomials called (𝑝,𝑞)-Fibonacci polynomials. We obtain combinatorial identities and by using Riordan method we get factorizations of Pascal matrix involving (𝑝,𝑞)-Fibonacci polynomials.

(p,q)

Abstract In [Acta Math. Hungar. 66 (1995), 337–343], Bell and Daif proved that if R is a prime ring admitting a nonzero derivation such that d(xy)=d(yx)

-Fibonacci and

{d(xy)=d(yx)}

(p,q)

for all x,y∈R

-Lucas Polynomials

{x,y\in R}

On derivations and commutativity of prime rings with involution

, then R is commutative. The objective of this paper is to examine similar problems when the ring R is equipped with involution. It is shown that if a prime ring R with involution * of a characteristic different from 2 admits a nonzero derivation d such that d(xx * )=d(x * x)

The Commutativity in Prime Gamma Rings with Left Derivation

{d(xx^*)=d(x^*x)}

Gaussian Jacobsthal And Gaussian Jacobsthal Lucas Numbers.

for all x ∈ R and S(R)∩Z(R)≠(0)

On Fibo-Pascal Matrix Involving k-Fibonacci and k-Pell Matrices

{S(R)\cap Z(R)\ne (0)}

Some Properties Of Bivariate Gaussian Fibonacci And Lucas p-Polynomials.

, then R is commutative. Moreover, some related results have also been discussed.