منابع مشابه
Flatness and the Ore Condition for Rings
We prove the following result on the universal localization of a ring R at an ideal I: If the universal localization is flat as an R-module, then R satisfies the Ore condition with respect to the multiplicative set of elements that become invertible modulo I. It is well known that for domains the converse of this result holds, and hence we have found in this case a new characterization of the O...
متن کاملAffine Schemes and Topological Closures in the Zariski-riemann Space of Valuation Rings
Let F be a field, let D be a subring of F , and let X be the Zariski-Riemann space of valuation rings containing D and having quotient field F . We consider the Zariski, inverse and patch topologies on X when viewed as a projective limit of projective integral schemes having function field contained in F , and we characterize the locally ringed subspaces of X that are affine schemes.
متن کاملSpectra, Spectra, Spectra – Tensor Triangular Spectra versus Zariski Spectra of Endomorphism Rings
We construct a natural continuous map from the triangular spectrum of a tensor triangulated category to the algebraic Zariski spectrum of the endomorphism ring of its unit object. We also consider graded and twisted versions of this construction. We prove that these maps are quite often surjective but far from injective in general. For instance, the stable homotopy category of finite spectra ha...
متن کاملFlatness and Torsion in Tensor Powers of Modules over Local Rings
This is a fairly literal transcript of my lectures at the 7th Japan-Vietnam Joint Seminar on Commutative Algebra, held in Quy Nhon, Vietnam, from 12th–16th December 2011. The aim of those lectures was to describe my recent work with Avramov [2] on a conjecture of Vasconcelos [18] concerning the relationship between flatness and torsion in tensor product of modules over regular rings, that in tu...
متن کاملFiber Products and Zariski Sheaves
Definition 1.1. Let C be a category, and X, Y, Z objects of C. Fix also morphisms πX : X → Z, πY : Y → Z. Given this data, we say that an object P of C, together with morphisms p1 : P → X, p2 : P → Y is a fiber product of X with Y over Z if it satisfies the following universal property: For every object T ∈ Obj(C), and every pair of morphisms f : T → X, g : T → Y such that πX ◦ f = πY ◦ g, ther...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1991
ISSN: 0021-8693
DOI: 10.1016/0021-8693(91)90176-9