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NOTE ON GOOD IDEALS IN GORENSTEIN LOCAL RINGS
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 Title & Authors
NOTE ON GOOD IDEALS IN GORENSTEIN LOCAL RINGS
Kim, Mee-Kyoung;
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 Abstract
Let I be an ideal in a Gorenstein local ring A with the maximal ideal m and d = dim A. Then we say that I is a good ideal in A, if I contains a reduction generated by d elements in A and of I is a Gorenstein ring with a(G(I)) = 1-d, where a(G(I)) denotes the a-invariant of G(I). Let S = A[Q/a] and P = mS. In this paper, we show that the following conditions are equivalent. (1) = QI and I = Q:I. (2) = IS and IS = S:sIS. (3) Sp = ISp and ISp = Sp :sp ISp. We denote by the set of good ideals I in such that I contains Q as a reduction. As a Corollary of this result, we show that .
 Keywords
Rees algebra;associated graded ring;Cohen-Macaulay ring, Gorenstein ring;a-invariant;
 Language
English
 Cited by
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