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Manuel L. Reyes 《Israel Journal of Mathematics》2012,192(2):667-698
This paper concerns contravariant functors from the category of rings to the category of sets whose restriction to the full subcategory of commutative rings is isomorphic to the prime spectrum functor Spec. The main result reveals a common characteristic of these functors: every such functor assigns the empty set to $\mathbb{M}_n (\mathbb{C})$ for n ? 3. The proof relies, in part, on the Kochen-Specker Theorem of quantum mechanics. The analogous result for noncommutative extensions of the Gel’fand spectrum functor for C*-algebras is also proved. 相似文献
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Gorenstein flatness and injectivity over Gorenstein rings 总被引:1,自引:0,他引:1
Let R be a Gorenstein ring.We prove that if I is an ideal of R such that R/I is a semi-simple ring,then the Gorenstein flat dimension of R/I as a right R-module and the Gorenstein injective dimension of R/I as a left R-module are identical.In addition,we prove that if R→S is a homomorphism of rings and SE is an injective cogenerator for the category of left S-modules,then the Gorenstein flat dimension of S as a right R-module and the Gorenstein injective dimension of E as a left R-module are identical.We also give some applications of these results. 相似文献
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Yuli B. Rudyak 《Proceedings of the American Mathematical Society》2002,130(5):1503-1506
We construct a right adjoint functor to the Thom functor, i.e., to the functor which assigns the Thom space to a vector bundle .
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The purpose of this note is to show that the only idempotent kernel functor σ on Mod-R, whereR is a semiprime ring andR
R has finite σ-length, is the idempotent kernel functorZ corresponding to the Goldie torsion theory. 相似文献
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Zi-hui Liu 《应用数学学报(英文版)》2011,27(1):141-148
The properties of the generator matrix are given for linear codes over finite commutative chain rings,and the so-called almost-MDS (AMDS) codes are studied. 相似文献
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Tadashi Ishii 《Topology and its Applications》1980,11(2):173-187
The main purpose of this paper is to settle the following problem concerning a product formula for the Tychonoff functor τ, by introducing the notion of w-compact spaces: Characterize a topological space X such that τ(X×Y)=τ(X)×τ(Y) for any topological space Y. We also study the properties of w-compact spaces, and it is proved that, for any family {Xα} of w-compact spaces, the product ΠXα is also w-compact and τ(ΠXα)=Πτ(Xα). 相似文献
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F. Guillén 《Topology and its Applications》2009,156(3):658-660
Let S∗ and be the functors of continuous and differentiable singular chains on the category of differentiable manifolds. We prove that the natural transformation , which induces homology equivalences over each manifold, is not a natural homotopy equivalence. 相似文献
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David Kirby 《代数通讯》2013,41(4):1229-1244
We show that Jordan triple homomorphisms and derivations between prime special quadral Jordan triple systems on which Zel’manov polynomials do not vanish extend to associative homomorphis and derivations of associative ?-envelopes (either associative triple systems or Z2-graded associative algebras). This generalizes results of Zel'manov and McCrimmon for Jordan algebras (which in turn generalized results of Martindale). 相似文献
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Mefharet Kocatepe 《Archiv der Mathematik》1985,44(5):438-445
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Using sheaf theoretic methods, we define functors and . The functor extends the one in [L. Barbieri-Viale, B. Kahn, On the derived category of 1-motives, I. Prépublication Mathématique de l’IHÉS (M/07/22), June 2007, 144 pages] to non-necessarily geometric motives. These functors are then used to define higher Néron-Severi groups and higher Albanese sheaves. 相似文献
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Let M be a left module for the Schur algebra S(n, r), and let \({s \in \mathbb{Z}^+}\) . Then \({M^{\otimes s}}\) is a \({(S(n,\,rs), F{\mathfrak{S}_{s}})}\) -bimodule, where the symmetric group \({{\mathfrak{S}_s}}\) on s letters acts on the right by place permutations. We show that the Schur functor f rs sends \({M^{\otimes s}}\) to the \({(F{\mathfrak{S}_{rs}},F{\mathfrak{S}_s})}\) -bimodule \({F\mathfrak{S}_{rs}\otimes_{F(\mathfrak{S}_{r}\wr{\mathfrak{S}_s})} ((f_rM)^{\otimes s}\otimes_{F} F{\mathfrak{S}_s})}\) . As a corollary, we obtain the image under the Schur functor of the Lie power L s (M), exterior power \({\bigwedge^s(M)}\) of M and symmetric power S s (M). 相似文献
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Consider a coring with exact rational functor, and a finitely generated and projective right comodule. We construct a functor
(coinduction functor) which is right adjoint to the hom-functor represented by this comodule. Using the coinduction functor, we establish a bijective
map between the set of representative classes of torsion simple right comodules and the set of representative classes of simple
right modules over the endomorphism ring. A detailed application to group-graded modules is also given. 相似文献
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Christian Brouder 《Journal of Pure and Applied Algebra》2007,209(2):477-495
The Hopf algebra of renormalization in quantum field theory is described at a general level. The products of fields at a point are assumed to form a bialgebra B and renormalization endows T(T(B)+), the double tensor algebra of B, with the structure of a noncommutative bialgebra. When the bialgebra B is commutative, renormalization turns S(S(B)+), the double symmetric algebra of B, into a commutative bialgebra. The usual Hopf algebra of renormalization is recovered when the elements of S1(B) are not renormalized, i.e., when Feynman diagrams containing one single vertex are not renormalized. When B is the Hopf algebra of a commutative group, a homomorphism is established between the bialgebra S(S(B)+) and the Faà di Bruno bialgebra of composition of series. The relation with the Connes-Moscovici Hopf algebra is given. Finally, the bialgebra S(S(B)+) is shown to give the same results as the standard renormalization procedure for the scalar field. 相似文献
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