共查询到20条相似文献,搜索用时 15 毫秒
1.
Shaun V. Ault 《Journal of Pure and Applied Algebra》2011,215(12):2847-2852
We examine the dual of the so-called “hit problem”, the latter being the problem of determining a minimal generating set for the cohomology of products of infinite projective spaces as a module over the Steenrod Algebra A at the prime 2. The dual problem is to determine the set of A-annihilated elements in homology. The set of A-annihilateds has been shown by David Anick to be a free associative algebra. In this note we prove that, for each k≥0, the set of kpartiallyA-annihilateds, the set of elements that are annihilated by Sqi for each i≤2k, itself forms a free associative algebra. 相似文献
2.
Classical homological algebra studies chain complexes, resolutions, and derived functors in additive categories. In this paper we define higher order chain complexes, resolutions, and derived functors in the context of a new type of algebraic structure, called an algebra of left cubical balls . We show that higher order resolutions exist in these algebras, and that they determine higher order Ext-groups. In particular, the Em-term of the Adams spectral sequence (m>2) is such a higher Ext-group, providing a new way of constructing its differentials. 相似文献
3.
Classical homological algebra takes place in additive categories. In homotopy theory such additive categories arise as homotopy categories of “additive groupoid enriched categories”, in which a secondary analog of homological algebra can be performed. We introduce secondary chain complexes and secondary resolutions leading to the concept of secondary derived functors. As a main result we show that the E3-term of the Adams spectral sequence can be expressed as a secondary derived functor. This result can be used to compute the E3-term explicitly by an algorithm. 相似文献
4.
In [3] well known results of Wall and Arnon on the monomial bases in the mod 2 Steenrod algebra (see [9], [1]) were generalized to the subalgebra of the mod p Steenrod algebra, , generated by the reduced powers. In the present paper we considered the case of the full Steenrod algebra . We constructed βX-, βZ-, βC-, ZA-, and XC-bases. We proved extremal properties of the βX-, βZ-, ZA-, and XC-bases. Also we constructed a new polynomial generators of the ring in terms of the βC-basis. 相似文献
5.
《Mathematische Nachrichten》2017,290(10):1512-1530
From certain triangle functors, called nonnegative functors, between the bounded derived categories of abelian categories with enough projective objects, we introduce their stable functors which are certain additive functors between the stable categories of the abelian categories. The construction generalizes a previous work by Hu and Xi. We show that the stable functors of nonnegative functors have nice exactness property and are compatible with composition of functors. This allows us to compare conveniently the homological properties of objects linked by the stable functors. In particular, we prove that the stable functor of a derived equivalence between two arbitrary rings provides an explicit triangle equivalence between the stable categories of Gorenstein projective modules. This generalizes a result of Y. Kato. Our results can also be applied to provide shorter proofs of some known results on homological conjectures. 相似文献
6.
Maurizio Brunetti Adriana Ciampella Luciano A. Lomonaco 《manuscripta mathematica》2005,118(3):271-282
The mod 2 universal Steenrod algebra Q is a homogeneous quadratic algebra closely related to the ordinary mod 2 Steenrod algebra and the Lambda algebra introduced
in [1]. In this paper we show that Q is Koszul. It follows by [7] that its cohomology, being purely diagonal, is isomorphic to a completion of Q itself with respect to a suitable chain of two-sided ideals. 相似文献
7.
8.
Pedro Nicolás 《Journal of Pure and Applied Algebra》2008,212(12):2633-2659
Curved A∞-algebras appear in nature as deformations of dg algebras. We develop the basic theory of curved A∞-algebras and, in particular, curved dg algebras. We investigate their link with a suitable class of dg coalgebras via the bar construction and produce Quillen model structures on their module categories. We define the analogue of the relative derived category for a curved dg algebra. 相似文献
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10.
For R a commutative Noetherian ring, wide and Serre subcategories of finitely generated R-modules have been classified by their support. This paper studies general torsion classes and introduces narrow subcategories. These are closed under fewer operations than wide and Serre subcategories, but still for finitely generated R-modules both narrow subcategories and torsion classes are classified using the same support data. Although for finitely generated R-modules all four kinds of subcategories coincide, they do not coincide in the larger category of all R-modules. 相似文献
11.
Nicholas J. Kuhn 《Mathematische Zeitschrift》2014,277(3-4):917-936
In the early 1990’s, Lionel Schwartz gave a lovely characterization of the Krull filtration of \({\mathcal {U}}\) , the category of unstable modules over the mod \(p\) Steenrod algebra. Soon after, this filtration was used by the author as an organizational tool in posing and studying some topological nonrealization conjectures. In recent years the Krull filtration of \({\mathcal {U}}\) has been similarly used by Castellana, Crespo, and Scherer in their study of H–spaces with finiteness conditions. Recently, Gaudens and Schwartz have given a proof of some of my conjectures. In light of these topological applications, it seems timely to better expose the algebraic properties of the Krull filtration. 相似文献
12.
A.D. Elmendorf 《Advances in Mathematics》2006,205(1):163-228
We give a new construction of the algebraic K-theory of small permutative categories that preserves multiplicative structure, and therefore allows us to give a unified treatment of rings, modules, and algebras in both the input and output. This requires us to define multiplicative structure on the category of small permutative categories. The framework we use is the concept of multicategory (elsewhere also called colored operad), a generalization of symmetric monoidal category that precisely captures the multiplicative structure we have present at all stages of the construction. Our method ends up in the Hovey-Shipley-Smith category of symmetric spectra, with an intermediate stop at a category of functors out of a particular wreath product. 相似文献
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14.
Assaf Libman 《Topology》2003,42(3):555-568
For a coaugmented functor J on spaces, we consider J-modules and finite J-limits. The former are spaces X which are retracts of JX via the natural map. The latter are homotopy limits of J-modules arranged in diagrams whose shape is finite dimensional. Familiar examples are generalised Eilenberg MacLane spaces, which are the SP∞-modules. Finite SP∞-limits are nilpotent spaces with a very strong finiteness property. We show that the cofacial Bousfield-Kan construction of the functors Jn is universal for finite J-limits in the sense that every map X→Y where Y is a finite J-limit, factors through such natural map X→JnX, for some n<∞. 相似文献
15.
Alessandro Ardizzoni 《Annali dell'Universita di Ferrara》2004,50(1):167-185
LetA be an algebra in an abelian monoidal category M. We prove that the category of leftA-modules is abelian, wheneverA is right coflat.
This paper was written while the author was member of G.N.S.A.G.A. with partial financial support from M.I.U.R. 相似文献
16.
Andrew Conner Ellen Kirkman James Kuzmanovich W. Frank Moore 《Journal of Pure and Applied Algebra》2014
Let A be a connected graded noncommutative monomial algebra. We associate to A a finite graph Γ(A) called the CPS graph of A. Finiteness properties of the Yoneda algebra ExtA(k,k) including Noetherianity, finite GK dimension, and finite generation are characterized in terms of Γ(A). We show that these properties, notably finite generation, can be checked by means of a terminating algorithm. 相似文献
17.
A topological proof is given that real compositions algebras of finite dimension greater than one are algebraically closed under polynomial equations with a tame tail. 相似文献
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19.
M.E. Petty 《Topology and its Applications》1982,14(1):71-85
Let R+ be the space of nonnegative real numbers. F. Waldhausen defines a k-fold end structure on a space X as an ordered k-tuple of continuous maps xf:X → R+, 1 ? j ? k, yielding a proper map x:X → (R+)k. The pairs (X,x) are made into the category Ek of spaces with k-fold end structure. Attachments and expansions in Ek are defined by induction on k, where elementary attachments and expansions in E0 have their usual meaning. The category Ek/Z consists of objects (X, i) where i: Z → X is an inclusion in Ek with an attachment of i(Z) to X, and the category Ek6Z consists of pairs (X,i) of Ek/Z that admit retractions X → Z. An infinite complex over Z is a sequence X = {X1 ? X2 ? … ? Xn …} of inclusions in Ek6Z. The abelian grou p S0(Z) is then defined as the set of equivalence classes of infinite complexes dominated by finite ones, where the equivalence relation is generated by homotopy equivalence and finite attachment; and the abelian group S1(Z) is defined as the set of equivalence classes of X1, where X ∈ Ek/Z deformation retracts to Z. The group operations are gluing over Z. This paper presents the Waldhausen theory with some additions and in particular the proof of Waldhausen's proposition that there exists a natural exact sequence 0 → S1(Z × R)→πS0(Z) by utilizing methods of L.C. Siebenmann. Waldhausen developed this theory while seeking to prove the topological invariance of Whitehead torsion; however, the end structures also have application in studying the splitting of a noncompact manifold as a product with R[1]. 相似文献
20.
M. C. Crabb 《Journal of Fixed Point Theory and Applications》2007,2(2):171-193
We describe an equivariant version (for actions of a finite group G) of Dold’s index theory, [10], for iterated maps. Equivariant Dold indices are defined, in general, for a G-map U → X defined on an open G-subset of a G-ANR X (and satisfying a suitable compactness condition). A local index for isolated fixed-points is introduced, and the theorem
of Shub and Sullivan on the vanishing of all but finitely many Dold indices for a continuously differentiable map is extended
to the equivariant case. Homotopy Dold indices, arising from the equivariant Reidemeister trace, are also considered.
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