A tight closure analogue of analytic spread

2005 Mathematical proceedings of the Cambridge Philosophical Society (Print)  
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
more » ... ave the same minimal number of generators. This number is called the $*$-spread of the ideal, by analogy with the notion of analytic spread.
doi:10.1017/s0305004105008546 fatcat:a5dav2w7ebcv7iarleqngh435y