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• W2073073663 abstract "The Briançon–Skoda theorem in its many versions has been studied by algebraists for several decades. In this paper, under some assumptions on an F-rational local ring ( R , m ) , and an ideal I of R of analytic spread ℓ and height g < ℓ , we improve on two theorems by Aberbach and Huneke. Let J be a reduction of I . We first give results on when the integral closure of I ℓ + w is contained in the product J w + 1 I [ ℓ − 1 ] , for any integer w ⩾ 0 , where, given any primary decomposition of I , I [ ℓ − 1 ] is the intersection of the primary components of I of height at most ℓ − 1 . In the case that R is also Gorenstein, we give results on when the integral closure of I ℓ − 1 is contained in J ." @default.
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• W2073073663 date "2011-11-01" @default.
• W2073073663 modified "2023-09-29" @default.
• W2073073663 title "A less restrictive Briançon–Skoda theorem with coefficients" @default.
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• W2073073663 doi "https://doi.org/10.1016/j.jalgebra.2011.08.016" @default.
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