RING EXTENSIONS AND THEIR QUOTIENT RINGS

Abstract

In this article we introduce a ring extension E(R)=R[x,σ,τ,δ] of a ring R and show that if R is an order in an artinian ring, then R[x,σ,τ,δ] is an order in an artinian ring, where σ and τ are automorphisms of R and δ is a (σ,τ)-derivation of R.