Alternative Derivations in (1,1) Rings

Abstract

Objectives: To show the associativity in one of the subclass of non-associative (γ,δ) rings. Method: Derivation alternator rings are limiting case of associative rings. The ring (1,1) is one of the sub class of (γ,δ) rings. Consider a (1,1) derivation alternator ring R, with characteristic ≠ 2, and it is well known that this ring is neither alternative nor flexible. In this paper it will be proved that right alternative property (R,x,x) holds in R and flexibility follows, finally associativity arrives in R. Findings: If this ring R does not contain nilpotent elements even though it will be associative. Novelty: Further investigators may extend the applications of these rings in science and engineering fields. Mathematics Subject Classification: 2010 MSC 17D