Diamond Closure

Melvin Hochster and Juan D. Vélez

A chapter in Algebra, Arithmetic and Geometry with Applications, 2004, pp 511-523 from Springer

Abstract: Abstract A closure operation is introduced for complete local domains of mixed characteristic p > 0 that has some, but not all, of the desired properties for a mixed characteristic analogue of tight closure. It provides information about what multiplies an element in a system of parameters into the ideal generated by its predecessors, under certain conditions, that is unavailable by other methods. The most serious defect of this notion is that not every ideal of a complete regular local ring need be closed. It is defined in terms of new type of “power” of an ideal introduced here.

Keywords: Local Ring; Noetherian Ring; Regular Ring; Integral Closure; Test Element (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/978-3-642-18487-1_29

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