منابع مشابه
2 00 9 Exact Zero Divisors and Free Resolutions over Short Local Rings
Let R be a local ring with maximal ideal m such that there exists a pair of elements a, b with (0 : a) = bR and (0 : b) = aR; we say that a pair a, b as above is an exact pair of zero divisors. We study minimal free resolutions of finitely generated R-modules M , with particular attention to the case when m = 0. Let e denote the minimal number of generators of m. If R is Gorenstein with m = 0 a...
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Projective resolutions of modules over a ring R are constructed starting from appropriate projective resolutions over a ring Q mapping to R. It is shown that such resolutions may be chosen to be minimal in codimension ≤ 2, but not in codimension 3. This is used to obtain minimal resolutions for essentially all modules over local (or graded) rings R with codimension ≤ 2. Explicit resolutions are...
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Let Q be an affine semigroup generating Z, and fix a finitely generated Z -graded module M over the semigroup algebra k[Q] for a field k. We provide an algorithm to compute a minimal Z-graded injective resolution of M up to any desired cohomological degree. As an application, we derive an algorithm computing the local cohomology modulesH I(M) supported on any monomial (that is, Z -graded) ideal...
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2008
ISSN: 0024-6107
DOI: 10.1112/jlms/jdn027