A tight closure analogue of analytic spread

NEIL M. EPSTEIN
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