On Ore Extensions Over Near Pseudo Valuation Rings

摘要

Let R be a commutative Noetherian ring which is also an algebra over Q, (Q is the field of rational numbers). Let σ be an automorphism of R and S a σ-derivation of R such that σ(δ(a)) δ(σ(a)), for all a∈ R. This paper concerns Ore extensions over near pseudo valuation rings (NPVR) and almost δ-divided rings. Towards this we prove: 1. If R is a near pseudo valuation ring, then O(R) = R[x;σ,δ] is a near pseudo valuation ring. 2. If R is an almost δ-divided ring, then O(R) = R[x; σ, δ] is an almost δ-divided ring. 1991 Mathematics Subject Classification. Primary 16-XX; Secondary 16N40, 16P40, 16S36.