Non-symmetry and symmetry of syzygies of a system of Cauchy functional equations with a homomorphism

Abstract

Two entirely different Cauchy functional equations have been investigated in the literature with a couple of unknown operators f and g mapping a unitary ring X into a domain of integrity Y satisfying the elimination law and keeping the operations of addition about operator f and multiplication about operator g, respectively. A total of four studying syzygies achieved by multiplying these two fundamental Cauchy functional equations side by side are investigated. The novelty of the literature is to find out sufficient conditions upon [Formula: see text] deriving the model to be produced a strongly alienation phenomenon by using some new computation techniques.

Keywords

• Symmetry
• functional equations
• new computation techniques
• the alienation phenomenon
• the Cauchy equation