RELATIVE ASCENT AND DESCENT IN A DOMAIN EXTENSION

Abstract

In this study we continue to investigate the ascent and descent of valuation domains, PVDs, GCD-domains, ∗-domains, ∗∗-domains, locally ∗- domains, URDs, UFDs, RBFDs, CK -domains, BVDs, CHFDs, and a particular case of LHFDs for domain extensions A ⊆ B relative to the Condition 1: “Let A ⊆ B be a unitary commutative ring extension. For each b ∈ B there exist u ∈ U(B) and a ∈ A such that b = au” and with the further assumption that the conductor ideal A : B is a maximal ideal in A.