A variant of Wang's theorem

JOURNAL OF ALGEBRA

卷:369

Article

Watanabe, Kei-ichi¹  Yoshida, Ken-ichi¹ 

[1] Nihon Univ, Coll Humanities & Sci, Dept Math, Setagaya Ku, Tokyo 1568550, Japan

关键词: Gorenstein ring;    Cohen-Macaulay ring;    Regular ring;    Test ideal;    Multiplier ideal;    Integral closure;    Goto number;   

DOI  :  10.1016/j.jalgebra.2012.07.012

来源: Elsevier

【 摘 要 】

In this paper, we give a new formula of J : (J) over bar for any parameter ideal J in a Gorenstein local ring R of positive characteristic in terms of test ideals: J : (J) over bar = J + tau (J(d-1)), where tau (J(d-1)) denotes the J(d-1)-test ideal of R. As an application, we give a variant of Wang's theorem. Namely, we prove that if J is a parameter ideal in a Cohen-Macaulay local ring (R, m) of dimension d >= 2 with J subset of m(s), then J : m((d-1)(s-1)) (resp. J : m((d-1)(s-1)+1)) is integral over J (resp. if R is not regular). Moreover, we prove that, after reduction to characteristic p >> 0, a similar assertion holds true for Cohen-Macaulay Q-Gorenstein normal local domain essentially of finite type over a field of characteristic zero under some extra assumption. (c) 2012 Elsevier Inc. All rights reserved.

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