共查询到20条相似文献,搜索用时 843 毫秒
1.
Edgar E. Enochs Juan Martí nez Herná ndez Alberto del Valle 《Proceedings of the American Mathematical Society》1998,126(6):1611-1620
The category of left modules over right coherent rings of finite weak global dimension has several nice features. For example, every left module over such a ring has a flat cover (Belshoff, Enochs, Xu) and, if the weak global dimension is at most two, every left module has a flat envelope (Asensio, Martínez). We will exploit these features of this category to study its objects. In particular, we will consider orthogonal complements (relative to the extension functor) of several classes of modules in this category. In the case of a commutative ring we describe an idempotent radical on its category of modules which, when the weak global dimension does not exceed 2, can be used to analyze the structure of the flat envelopes and of the ring itself.
2.
Elton Pasku 《Semigroup Forum》2011,83(1):75-88
We prove that the category of Clifford semigroups and prehomomorphisms CSP\mathcal{CSP} is isomorphic to a certain subcategory of the category of diagrams over groups. Under this isomorphism, Clifford semigroups
are identified with certain functors. As an application of the isomorphism theorem, we show that the category with objects
commutative inverse semigroups having the same semilattice of idempotents and with morphisms, the inverse semigroup homomorphisms
that fix the semilattice, imbeds into a category of right modules over a certain ring. Also we find a very close relationship
between the cohomology groups of a commutative inverse monoid and the cohomology groups of the colimit group of the functor
giving the monoid. 相似文献
3.
We show that the Hilbert functor of rank one families on a non-separated scheme X admits deformations that are not effective. For such ambient schemes we have that the Hilbert functor is not representable
by a scheme or an algebraic space. 相似文献
4.
Roberto Martínez Villa 《代数通讯》2013,41(10):3941-3973
A contravariant functor is constructed from the stable projective homotopy theory of finitely generated graded modules over a finite-dimensional algebra to the derived category of its Yoneda algebra modulo finite complexes of modules of finite length. If the algebra is Koszul with a noetherian Yoneda algebra, then the constructed functor is a duality between triangulated categories. If the algebra is self-injective, then stable homotopy theory specializes trivially to stable module theory. In particular, for an exterior algebra the constructed duality specializes to (a contravariant analog of) the Bernstein–Gelfand–Gelfand correspondence. 相似文献
5.
Jyh-Haur Teh 《代数通讯》2013,41(5):1800-1824
We study families of algebraic varieties parametrized by topological spaces and generalize some classical results such as Hilbert Nullstellensatz and primary decomposition of commutative rings. We show that there is an equivalence between the category of bivariant coherent sheaves and the category of sheaves of finitely generated modules. 相似文献
6.
We will generalize the projective model structure in the categoryof unbounded complexes of modules over a commutative ring tothe category of unbounded complexes of quasi-coherent sheavesover the projective line. Concretely we will define a locallyprojective model structure in the category of complexes of quasi-coherentsheaves on the projective line. In this model structure thecofibrant objects are the dg-locally projective complexes. Wealso describe the fibrations of this model structure and showthat the model structure is monoidal. We point out that thismodel structure is necessarily different from other known modelstructures such as the injective model structure and the locallyfree model structure. 相似文献
7.
For all subgroups H of a cyclic p-group G we define norm functors that build a G-Mackey functor from an H-Mackey functor. We give an explicit construction of these functors in terms of generators and relations based solely on the intrinsic, algebraic properties of Mackey functors and Tambara functors. We use these norm functors to define a monoidal structure on the category of Mackey functors where Tambara functors are the commutative ring objects. 相似文献
8.
David Rydh 《代数通讯》2013,41(7):2632-2646
We show that the Hilbert functor of points on an arbitrary separated algebraic stack is an algebraic space. We also show the algebraicity of the Hilbert stack of points on an algebraic stack and the algebraicity of the Weil restriction of an algebraic stack along a finite flat morphism. For the latter two results, no separation assumptions are necessary. 相似文献
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11.
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
12.
We discuss properties of Yetter-Drinfeld modules over weak bialgebras over commutative rings. The categories of left-left, left-right, right-left and right-right Yetter-Drinfeld modules over a weak Hopf algebra are isomorphic as braided monoidal categories. Yetter-Drinfeld modules can be viewed as weak Doi-Hopf modules, and, a fortiori, as weak entwined modules. IfH is finitely generated and projective, then we introduce the Drinfeld double using duality results between entwining structures and smash product structures, and show that the category of Yetter-Drinfeld modules is isomorphic to the category of modules over the Drinfeld double. The category of finitely generated projective Yetter-Drinfeld modules over a weak Hopf algebra has duality. 相似文献
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14.
R. G. Larson 《Applied Categorical Structures》1998,6(2):139-150
The relation between a monoidal category which has an exact faithful monoidal functor to a category of finite rank projective modules over a Dedekind domain, and the category of continuous modules over a topological bialgebra is discussed. If the monoidal category is braided, the bialgebra is topologically quasitriangular. If the monoidal category is rigid monoidal, the bialgebra is a Hopf algebra. 相似文献
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16.
Luchezar L. Avramov Ragnar-Olaf Buchweitz Srikanth Iyengar 《Inventiones Mathematicae》2007,169(1):1-35
A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules
over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class – a substitute
for the length of a free complex – and on the rank of a differential module in terms of invariants of its homology. These
results specialize to basic theorems in commutative algebra and algebraic topology. One instance is a common generalization
of the equicharacteristic case of the New Intersection Theorem of Hochster, Peskine, P. Roberts, and Szpiro, concerning complexes
over commutative noetherian rings, and of a theorem of G. Carlsson on differential graded modules over graded polynomial rings. 相似文献
17.
A natural question in the theory of Tannakian categories is: What if you don’t remember Forget? Working over an arbitrary commutative ring R, we prove that an answer to this question is given by the functor represented by the étale fundamental groupoid π 1(spec(R)), i.e. the separable absolute Galois group of R when it is a field. This gives a new definition for étale π 1(spec(R)) in terms of the category of R-modules rather than the category of étale covers. More generally, we introduce a new notion of “commutative 2-ring” that includes both Grothendieck topoi and symmetric monoidal categories of modules, and define a notion of π 1 for the corresponding “affine 2-schemes.” These results help to simplify and clarify some of the peculiarities of the étale fundamental group. For example, étale fundamental groups are not “true” groups but only profinite groups, and one cannot hope to recover more: the “Tannakian” functor represented by the étale fundamental group of a scheme preserves finite products but not all products. 相似文献
18.
We use techniques from both real and complex algebraic geometry to study K-theoretic and related invariants of the algebra C(X) of continuous complex-valued functions on a compact Hausdorff topological space X. For example, we prove a parameterized version of a theorem by Joseph Gubeladze; we show that if M is a countable, abelian, cancellative, torsion-free, semi-normal monoid, and X is contractible, then every finitely generated projective module over C(X)[M] is free. The particular case gives a parameterized version of the celebrated theorem proved independently by Daniel Quillen and Andrei Suslin that finitely
generated projective modules over a polynomial ring over a field are free. The conjecture of Jonathan Rosenberg which predicts
the homotopy invariance of the negative algebraic K-theory of C(X) follows from the particular case . We also give algebraic conditions for a functor from commutative algebras to abelian groups to be homotopy invariant on
C
*-algebras, and for a homology theory of commutative algebras to vanish on C
*-algebras. These criteria have numerous applications. For example, the vanishing criterion applied to nil K-theory implies that commutative C
*-algebras are K-regular. As another application, we show that the familiar formulas of Hochschild–Kostant–Rosenberg and Loday–Quillen for
the algebraic Hochschild and cyclic homology of the coordinate ring of a smooth algebraic variety remain valid for the algebraic
Hochschild and cyclic homology of C(X). Applications to the conjectures of Beĭlinson-Soulé and Farrell–Jones are also given. 相似文献