Gorenstein graded rings associated to ideals
نویسندگان
چکیده
منابع مشابه
Graded Rings Associated with Contracted Ideals
The study of the ideals in a regular local ring (R,m) of dimension 2 has a long and important tradition dating back to the fundamental work of Zariski [ZS]. More recent contributions are due to several authors including Cutkosky, Huneke, Lipman, Sally and Tessier among others, see [C1, C2, H, HS, L, LT]. One of the main result in this setting is the unique factorization theorem for complete (i....
متن کاملThe Gorenstein and Complete Intersection Properties of Associated Graded Rings
Let I be an m-primary ideal of a Noetherian local ring (R,m). We consider the Gorenstein and complete intersection properties of the associated graded ring G(I) and the fiber cone F (I) of I as reflected in their defining ideals as homomorphic images of polynomial rings over R/I and R/m respectively. In case all the higher conormal modules of I are free over R/I , we observe that: (i) G(I) is C...
متن کاملGood Ideals in Gorenstein Local Rings
Let I be an m-primary ideal in a Gorenstein local ring (A,m) with dimA = d, and assume that I contains a parameter ideal Q in A as a reduction. We say that I is a good ideal in A if G = ∑ n≥0 I n/In+1 is a Gorenstein ring with a(G) = 1−d. The associated graded ring G of I is a Gorenstein ring with a(G) = −d if and only if I = Q. Hence good ideals in our sense are good ones next to the parameter...
متن کاملNormal Ideals of Graded Rings
For a graded domain R = k[X0, ...,Xm]/J over an arbitrary domain k, it is shown that the ideal generated by elements of degree ≥ mA, where A is the least common multiple of the weights of the Xi, is a normal ideal.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2005
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2005.03.035