Akademik Veri Yönetim Sistemi
JOURNAL OF INFORMATION & OPTIMIZATION SCIENCES, cilt.46, sa.5, ss.1569-1585, 2025 (ESCI)
It is known that the quaternion algebras are central simple algebras and also clifford algebras. In this paper, we introduce a new class of quaternions called Lucas-Leonardo p-quaternions and derive several fundamental properties of these numbers. Furthermore, we investigate some applications related to companion sequences associated with Leonardo quaternions. In particular, we determine Lucas-Leonardo quaternions and Francois quaternions, which are zero divisors and invertible elements in the quaternion algebra over certain finite fields.