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Codimension, multiplicity and integral extensions

  • ARON SIMIS (a1), BERND ULRICH (a2) and WOLMER V. VASCONCELOS (a3)
    • Published online: 01 March 2001
Abstract

Let AB be a homogeneous inclusion of standard graded algebras with A0 = B0. To relate properties of A and B we intermediate with another algebra, the associated graded ring G = grA1B(B). We give criteria as to when the extension AB is integral or birational in terms of the codimension of certain modules associated to G. We also introduce a series of multiplicities associated to the extension AB. There are applications to the extension of two Rees algebras of modules and to estimating the (ordinary) multiplicity of A in terms of that of B and of related rings. Many earlier results by several authors are recovered quickly.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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