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A tight closure analogue of analytic spread

  • NEIL M. EPSTEIN (a1)

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.

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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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