کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4586006 | 1334080 | 2012 | 33 صفحه PDF | دانلود رایگان |
This paper is concerned with existence of big tight closure test elements for a commutative Noetherian ring R of prime characteristic p. Let R∘ denote the complement in R of the union of the minimal prime ideals of R. A big test element for R is an element of R∘ which can be used in every tight closure membership test for every R-module, and not just the finitely generated ones. The main results of the paper are that, if R is excellent and satisfies condition (R0), and c∈R∘ is such that Rc is Gorenstein and weakly F-regular, then some power of c is a big test element for R if (i) R is a homomorphic image of an excellent regular ring of characteristic p for which the Frobenius homomorphism is intersection-flat, or (ii) R is F-pure, or (iii) R is local. The Gamma construction is not used.
Journal: Journal of Algebra - Volume 349, Issue 1, 1 January 2012, Pages 284-316