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A tight closure analogue of analytic spread

Published online by Cambridge University Press:  05 September 2005

NEIL M. EPSTEIN
Affiliation:
Department of Mathematics, University of Kansas, Lawrence, KS 66045, U.S.A. e-mail: epstein@math.ku.edu

Abstract

An analogue of the theory of integral closure and reductions is developed for a more general class of closures, called Nakayama closures. It is shown that tight closure is a Nakayama closure by proving a “Nakayama lemma for tight closure”. Then, after strengthening A. Vraciu's theory of *-independence and the special part of tight closure, it is shown that all minimal *-reductions of an ideal in an analytically irreducible excellent local ring of positive characteristic have the same minimal number of generators. This number is called the *-spread of the ideal, by analogy with the notion of analytic spread.

Type
Research Article
Copyright
2005 Cambridge Philosophical Society

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