RELATIVE ASCENT AND DESCENT IN A DOMAIN EXTENSION

Year 2010, Volume: 7 Issue: 7, 34 - 46, 01.06.2010

Tariq Shah

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.

Keywords

conductor ideal, atomic domain, ascent, descent

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• Department of Mathematics Quaid-i-Azam University Islamabad, Pakistan e-mail: [e-mail]