منابع مشابه
Good 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...
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Denote by R the power series ring in countably many variables over a eld K; then R 0 is the smallest sub-algebra of R that contains all homogeneous elements. It is a fact that a homogeneous, nitely generated ideal J in R 0 have an initial ideal gr(J), with respect to an arbitrary admissible order, that is locally nitely generated in the sense that dimK gr(J) d P d?1 j=1 R 0 j gr(J) d?j < 1 for ...
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Koszul property was generalized to homogeneous algebras of degree N > 2 in [5], and related to N -complexes in [7]. We show that if the N -homogeneous algebra A is generalized Koszul, AS-Gorenstein and of finite global dimension, then one can apply the Van den Bergh duality theorem [23] to A, i.e., there is a Poincaré duality between Hochschild homology and cohomology of A, as for N = 2. Mathem...
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An ideal / in a commutative noetherian ring R is a Gorenstein ideal of grade g if pdR(R/I) = grade I = g and the canonical module HxtsR(R/I, R) is cyclic. Serre showed that if g = 2 then / is a complete intersection, and Buchsbaum and Eisenbud proved a structure theorem for the case g = 3. We present generic resolutions for a class of Gorenstein ideals of grade 4, and we illustrate the structur...
متن کاملGorenstein Algebras, Symmetric Matrices, Self-linked Ideals, and Symbolic Powers
Inspired by recent work in the theory of central projections onto hypersurfaces, we characterize self-linked perfect ideals of grade 2 as those with a Hilbert–Burch matrix that has a maximal symmetric subblock. We also prove that every Gorenstein perfect algebra of grade 1 can be presented, as a module, by a symmetric matrix. Both results are derived from the same elementary lemma about symmetr...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2014
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2013.11.015