Maps on Divisor Class Groups Induced by Ring Homomorphisms of Finite Flat Dimension

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/231191Let f: A\to B be a ring homomorphism between Noetherian normal integral domains. We establish a general criterion for f to induce a homomorphism Cl(f): Cl(A)\to Cl(B) on divisor class groups. For instance, this criterion applies whenever f has finite flat dimension; this special case generalizes the more classical situations where f is flat or is surjective with kernel generated by an A-regular element. We extend some of Spiroff's work on the kernels of induced maps to this more general setting.17 pages, uses xypic; v4 contains minor changes; final version to appear in Journal of Commutative AlgebraCommutative Algebra13C20 (Primary) 13B22, 13F40 (Secondary)Maps on Divisor Class Groups Induced by Ring Homomorphisms of Finite Flat Dimensiontext