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

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

2008-10-15

arxiv.org/abs/0810.2810v4

Mathematics

Commutative Algebra

17 pages, uses xypic; v4 contains minor changes; final version to appear in Journal of Commutative Algebra

Scientific paper

Let 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.

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