Tight closure and continuous closure
|Mathematics; Tight closure
|ACADEMIC PRESS INC ELSEVIER SCIENCE
|JOURNAL OF ALGEBRA
We show that for excellent, normal equicharacteristic rings with perfect residue fields the tight closure of an ideal is contained in its axes closure. First we prove this for rings in characteristic p. This is achieved by using the notion of special tight closure established by Huneke and Vraciu. By reduction to positive characteristic we show that the containment of tight closure in axes closure also holds in characteristic 0. From this we deduce that for a normal ring of finite type over C the tight closure of a primary ideal is inside its continuous closure. (C) 2019 Elsevier Inc. All rights reserved.
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