A tight closure analogue of analytic spread

Details A tight closure analogue of analytic spread A tight closure analogue of analytic spread

2004-06-09

arxiv.org/abs/math/0406160v1

Mathematical Proceedings of the Cambridge Philosophical Society, Volume 139, Issue 02, September 2005, pp 371-383

Mathematics

Commutative Algebra

16 pages

Scientific paper

10.1017/S0305004105008546

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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