About Some Split Central Simple Algebras

Abstract

In this paper we study certain quaternion algebras and symbol algebras which split.

Some properties of Fibonacci numbers, Fibonacci octonions, and generalized Fibonacci-Lucas octonions

“…Proposition 2.2. ( [Fl,Sa;14], [Fl,Sa,Io;13]) Let (f n ) n≥0 be the Fibonacci sequence and let (l n ) n≥0 be the Lucas sequence. Then:…”

“…Ci; 09], [Fl,Sa;15 ], [Fl,Sa;15 (a)]), [Ke,Ak;15], [Ke,Ak;15 (a)], [Ta;13]. In the paper [Ke,Ak;15 (a)], O. Kecilioglu, I. Akkus gave some properties of the split Fibonacci and Lucas octonions in the octonion algebra O(1, 1, −1) .…”

“…In this paper we study the Fibonacci octonions in certain generalized octonion algebras. In the paper [Fl,Sa;15 (a)], we introduced the generalized Fibonacci -Lucas quaternions and we determined some properties of these elements. In this paper we introduce the generalized Fibonacci -Lucas octonions and we prove that these elements have similar properties with the properties of the generalized Fibonacci -Lucas quaternions.…”

Codes Over a Subset of Octonion Integers

“…Proposition 2.5. [3,16] Let p ∈ N be a prime number. There are integers a, b such that p = a 2 + ab + 2b 2 if p = 7k + 1, k ∈ Z.…”

Codes Over Subsets of Algebras Obtained by the Cayley–Dickson Process

“…We will consider codes of length n = p−1 M . The below definitions and Theorems adapted and generalized to all algebras obtained by the Cayley-Dickson process some definitions from [Gu;13], [Ne,In,Fa,Pa;01], [Fl;15] and Theorems 7,8,9,10,11,13,14,15 from [Ne,In,Fa,Pa;01], Theorems 4,5,6,7 from [Gu; 13] and Theorems 2.3, 2.5, 2.7, 2.9 from [Fl;15].…”