Tight closure in non-excellent rings

Autor: Raymond C. Heitmann
Rok vydání: 2010
Předmět:
Zdroj: Journal of Algebra. 324(3):430-441
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2009.12.018
Popis: Some examples are constructed to demonstrate that tight closure need not satisfy several key properties when the ring is not excellent. In particular, there are counterexamples to colon-capturing and persistence. A consequence is that R + need not be Cohen–Macaulay when R is a local ring of characteristic p even when R is universally catenarian. A new closure operation for non-excellent local rings of characteristic p is introduced and it is seen to have most of the properties associated with tight closure.
Databáze: OpenAIRE
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