A tight closure analogue of analytic spread
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 *-indep...
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| Veröffentlicht in: | Mathematical proceedings of the Cambridge Philosophical Society 2005-09, Vol.139 (2), p.371-383 |
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| container_title | Mathematical proceedings of the Cambridge Philosophical Society |
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| creator | EPSTEIN, NEIL M. |
| description | 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. |
| doi_str_mv | 10.1017/S0305004105008546 |
| format | Article |
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| title | A tight closure analogue of analytic spread |
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