(– 1, 1) ring of degree five satisfying the identity (x, yz, w) = y(x, z, w).

Abstract

In this paper we describe (– 1, 1) ring of degree-5. We derive the condition for associativity of a third power associative (– 1, 1) ring of degree five satisfying the identity (x, yz, w) = y(x, z, w). The ring is also associative even when we induce the condition of the semiprimeness.