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Numerical criteria for integral dependence

Published online by Cambridge University Press:  27 April 2011

BERND ULRICH  and
JAVID VALIDASHTI
BERND ULRICH
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN 47907, U.S.A. e-mail: ulrich@math.purdue.edu
JAVID VALIDASHTI
Affiliation:
Department of Mathematics, University of Kansas, Lawrence, KS 66045, U.S.A. e-mail: jvalidas@math.ku.edu
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Abstract

We study multiplicity based criteria for integral dependence of modules or of standard graded algebras, known as ‘Rees criteria’. Rather than using the known numerical invariants, we achieve this goal with a more direct approach by introducing a multiplicity defined as a limit superior of a sequence of normalized lengths; this multiplicity is a non-negative real number that can be irrational.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 151 , Issue 1 , July 2011 , pp. 95 - 102
Copyright
Copyright © Cambridge Philosophical Society 2011

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References

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