Numerical criteria for integral dependence

BERND ULRICH, JAVID VALIDASHTI
2011 Mathematical proceedings of the Cambridge Philosophical Society (Print)  
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.
doi:10.1017/s0305004111000144 fatcat:mc4ulbuucrae5bu4c2wiaqn6oa