Normal transversality and uniform bounds

Details Normal transversality and uniform bounds Normal transversality and uniform bounds

1999-06-30

arxiv.org/abs/math/9906208v1

Mathematics

Commutative Algebra

12 pages, Latex

Scientific paper

For two ideals $I$ and $J$ of a noetherian ring, we characterize, in terms of the vanishing of Tor modules, when the associated graded ring of the sum $I+J$ is isomorphic to the tensor product of the associated graded ring of $I$ and the associated graded ring of $J$. It is shown that the relation type of the tensor product of two standard algebras is bounded above by the maximum of the relation type of each algebra. As a consequence, we deduce a uniform bound for the relation type of maximal ideals of an excellent ring and a classical result of Duncan and O'Carroll on the strong uniform Artin-Rees property.

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