共查询到20条相似文献,搜索用时 0 毫秒
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Let (R, m) be a complete Noetherian local ring, I an ideal of R and M a nonzero Artinian R-module. In this paper it is shown that if p is a prime ideal of R such that dim R/p = 1 and (0:M p) is not finitely generated and for each i ? 2 the R-module Ext R i (M,R/p) is of finite length, then the R-module Ext R 1 (M, R/p) is not of finite length. Using this result, it is shown that for all finitely generated R-modules N with Supp(N) ? V (I) and for all integers i ? 0, the R-modules Ext R i (N,M) are of finite length, if and only if, for all finitely generated R-modules N with Supp(N) ? V (I) and for all integers i ? 0, the R-modules Ext R i (M,N) are of finite length. 相似文献
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《Journal of Pure and Applied Algebra》2022,226(12):107109
We prove the existence of various adelic-style models for rigidly small-generated tensor-triangulated categories whose Balmer spectrum is a one-dimensional Noetherian topological space. This special case of our general programme of giving adelic models is particularly concrete and accessible, and we illustrate it with examples from algebra, geometry, topology and representation theory. 相似文献
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Fedor A. Bogomolov Paolo Cascini Bruno de Oliveira 《Central European Journal of Mathematics》2006,4(2):194-208
We prove that any finite set of n-dimensional isolated algebraic singularities can be afforded on a simply connected projective
variety.
The first author was partially supported by NSF grant DMS-01591 and the third author was partially supported by NSF grant
DMS-03693 相似文献
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Takao Fujita 《Inventiones Mathematicae》1981,64(1):119-121
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Diana Rodelo 《Journal of Pure and Applied Algebra》2012,216(8-9):1879-1886
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In o‐minimal structures, every cell is definably connected and every definable set is a finite union of its definably connected components. In this note, we introduce pseudo definably connected definable sets in weakly o‐minimal structures having strong cell decomposition, and prove that every strong cell in those structures is pseudo definably connected. It follows that every definable set can be written as a finite union of its pseudo definably connected components. We also show that the projections of pseudo definably connected definable sets are pseudo definably connected. Finally, we compare pseudo definable connectedness with (recently introduced) weak definable connectedness of definable sets in weakly o‐minimal structures. 相似文献
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Peter Hauber 《manuscripta mathematica》1994,83(1):265-277
This paper consists of two independent parts. First I give a Chern class condition that is sufficient for a smooth surface
in affinen-space to be a set-theoretic complete intersection. In the second part I show the existence of a smooth affine fourfold over
C which is not a complete intersection in anyA
n although its canonical bundle is trivial. 相似文献
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David Cox Alicia Dickenstein 《Proceedings of the American Mathematical Society》2005,133(11):3153-3162
Let be a complete toric variety with homogeneous coordinate ring . In this article, we compute upper and lower bounds for the codimension in the critical degree of ideals of generated by homogeneous polynomials that do not vanish simultaneously on .
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An algebra is affine complete iff its polynomial operations are the same as all the operations over its universe that are compatible with all its congruences.
A variety is affine complete iff all its algebras are. We prove that every affine complete variety is congruence distributive,
and give a useful characterization of all arithmetical, affine complete varieties of countable type. We show that affine complete
varieties with finite residual bound have enough injectives. We also construct an example of an affine complete variety without
finite residual bound.? We prove several results concerning residually finite varieties whose finite algebras are congruence
distributive, while leaving open the question whether every such variety must be congruence distributive.
Received February 28, 1997; accepted in final form December 9, 1997. 相似文献
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Damiano Testa 《Mathematische Zeitschrift》2008,259(1):61-64
Let be a smooth complex complete intersection such that . Let f : S → X be a generically finite morphism from a smooth projective variety to X. Under some positivity assumption on the anticanonical divisor of S, if 2 ≤ dim S ≤ dim X − 2 we prove that the deformations of f are contained in a subvariety of codimension at least 2. 相似文献
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Kalle Kaarli 《Algebra Universalis》1992,29(4):495-502
In [4] A. F. Pixley stated a problem due to A. L. Foster: is a functionally complete algebra having no non-trivial subalgebras necessarily categorical? In this paper we show that, in general, the answer to this question is negative. However the answer becomes affirmative, if we replace the word “non-trivial” by the word “proper”. 相似文献
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Edward Formanek 《代数通讯》2013,41(1):79-85
Rings are associative and have a unit and subrings are assumed to have the same unit. Ring homomorphisms are unitary, as are modules. Ideal means two-sided ideal. 相似文献
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Petter Andreas Bergh 《Proceedings of the American Mathematical Society》2007,135(12):3795-3803
Let be a complete intersection of codimension , and let be the algebraic closure of . We show that every homogeneous algebraic subset of is the cohomological support variety of an -module, and that the projective variety of a complete indecomposable maximal Cohen-Macaulay -module is connected.