WHEN DOES A RING EXTENSION OF A GOING-DOWN DOMAIN SATISFY GOING-DOWN?

Year 2010, Volume: 7 Issue: 7, 87 - 94, 01.06.2010

David E. Dobbs

Abstract

If R is a going-down domain and T is a commutative unital ring extension of R, then R ⊆ T satisfies going-down if and only if the associated reduced ring of T is a torsion-free R-module.

Keywords

going-down, ring extension, integral domain, commutative ring, going-down domain, locally divided domain, torsion-free module, associated reduced ring, total quotient ring