Commutative part of skew polynomial ring over split-octonion

Abstract

Let R be a ring. The set of polynomials R[x: σ] forms a ring with multiplication rule σ(a)x for all a ∈ R where σ is an endomorphism on R. In this paper R is the ring split octonion. Split octonion is an anti-commutative 8-dimensional alternative ring. In this paper, the commutative part of that ring over spilt octonion ring is determined.