| 1. |
- Lundström, Patrik, 1971-
(författare)
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Cohomology and Self-dual Normal Bases for Infinite Galois Field Extensions
- 2002
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Ingår i: Journal of Algebra. - 0021-8693 .- 1090-266X. ; 256, s. 531-541
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Tidskriftsartikel (refereegranskat)abstract
- We generalize an injectivity result obtained by Bayer-Fluckiger and Lenstra concerning pointed cohomology sets, defined by norm-one groups of finite-dimensional algebras with involution over fields k of characteristic different from 2, to the case of inverse limits of finite-dimensional k-algebras with involution. We use this generalization to obtain a result about self-dual normal bases for infinite Galois field extensions.
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| 2. |
- Skjelnes, Roy Mikael, et al.
(författare)
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Infinite intersections of open subschemes and the Hilbert scheme of points
- 2004
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Ingår i: Journal of Algebra. - : Elsevier BV. - 0021-8693 .- 1090-266X. ; 273:2, s. 571-585
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Tidskriftsartikel (refereegranskat)abstract
- We study infinite intersections of open subschemes and the corresponding infinite intersection of Hilbert schemes. If {U-alpha} is the collection of open subschemes of a variety X containing the fixed point P, then we show that the Hilbert functor of flat and finite families of Spec(O-X,O- P) = boolean AND(alpha) U-alpha is given by the infinite intersection boolean AND(alpha) Hilb(Ualpha), where Hilb(Ualpha), is the Hilbert functor of flat and finite families on U-alpha. In particular, we show that the Hilbert functor of flat and finite families on Spec(O-X,O- P) is representable by a scheme.
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| 3. |
- Abdallah, Nancy, et al.
(författare)
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Lefschetz properties of some codimension three Artinian Gorenstein algebras
- 2023
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Ingår i: Journal of Algebra. - : Elsevier BV. - 0021-8693 .- 1090-266X. ; 625, s. 28-45
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Tidskriftsartikel (refereegranskat)abstract
- Codimension two Artinian algebras have the strong and weak Lefschetz properties provided the characteristic is zero or greater than the socle degree. It is open to what extent such results might extend to codimension three Artinian Gorenstein algebras. Despite much work, the strong Lefschetz property for codimension three Artinian Gorenstein algebra has remained largely mysterious; our results build on and strengthen some of the previous results. We here show that every standard-graded codimension three Artinian Gorenstein algebra A having maximum value of the Hilbert function at most six has the strong Lefschetz property, provided that the characteristic is zero. When the characteristic is greater than the socle degree of A, we show that A is almost strong Lefschetz, they are strong Lefschetz except in the extremal pair of degrees.
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| 4. |
- Agerholm, Troels, et al.
(författare)
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On selfadjoint functors satisfying polynomial relations
- 2011
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Ingår i: Journal of Algebra. - : Elsevier BV. - 0021-8693 .- 1090-266X. ; 330:1, s. 448-467
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Tidskriftsartikel (refereegranskat)abstract
- We study selfadjoint functors acting on categories of finite dimensional modules over finite dimensional algebras with an emphasis on functors satisfying some polynomial relations. Selfadjoint functors satisfying several easy relations, in particular, idempotents and square roots of a sum of identity functors. are classified. We also describe various natural constructions for new actions using external direct sums, external tensor products. Serre subcategories, quotients and centralizer subalgebras.
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| 5. |
- Aghapournahr, Moharram, et al.
(författare)
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Local cohomology and Serre subcategories
- 2008
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Ingår i: Journal of Algebra. - : Elsevier BV. - 0021-8693 .- 1090-266X. ; 320:3, s. 1275-1287
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Tidskriftsartikel (refereegranskat)abstract
- The membership of the local cohomology modules H-a(n) (M) of a module M in certain Serre subcategories of the category of modules is studied from below (i < n) and from above (i > n). Generalizations of depth and regular sequences are defined. The relation of these notions to local cohomology are found. It is shown that the membership of the local cohomology modules of a finite module in a Serre subcategory in the upper range just depends on the support of the module. (C) 2008 Elsevier Inc. All rights reserved.
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| 6. |
- Alonso, M. E., et al.
(författare)
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Revisiting Zariski Main Theorem from a constructive point of view
- 2014
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Ingår i: Journal of Algebra. - : Elsevier BV. - 0021-8693 .- 1090-266X. ; 406, s. 46-68
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Tidskriftsartikel (refereegranskat)abstract
- This paper deals with the Peskine version of Zariski Main Theorem published in 1965 and discusses some applications. It is written in the style of Bishop's constructive mathematics. Being constructive, each proof in this paper can be interpreted as an algorithm for constructing explicitly the conclusion from the hypothesis. The main non-constructive argument in the proof of Peskine is the use of minimal prime ideals. Essentially we substitute this point by two dynamical arguments; one about gcd's, using subresultants, and another using our notion of strong transcendence. In particular we obtain algorithmic versions for the Multivariate Hensel Lemma and the structure theorem of quasi-finite algebras. (C) 2014 Elsevier Inc. All rights reserved.
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| 7. |
- Alsaody, Seidon
(författare)
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Classification of the Finite-Dimensional Real Division Composition Algebras having a Non-Abelian Derivation Algebra
- 2016
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Ingår i: Journal of Algebra. - : Elsevier BV. - 0021-8693 .- 1090-266X. ; 445, s. 35-77
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- We classify the category of finite-dimensional real division composition algebras having a non-abelian Lie algebra of derivations. Our complete and explicit classification is largely achieved by introducing the concept of a quasi-description of a category, and using it to express the problem in terms of normal form problems for certain group actions on products of 3-spheres.
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| 8. |
- Alsaody, Seidon, 1986, et al.
(författare)
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Lie bialgebras, fields of cohomological dimension at most 2 and Hilbert's Seventeenth Problem
- 2017
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Ingår i: Journal of Algebra. - : Elsevier BV. - 0021-8693 .- 1090-266X. ; 476, s. 368-394
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Tidskriftsartikel (refereegranskat)abstract
- © 2016 Elsevier Inc.We investigate Lie bialgebra structures on simple Lie algebras of non-split type A. It turns out that there are several classes of such Lie bialgebra structures, and it is possible to classify some of them. The classification is obtained using Belavin–Drinfeld cohomology sets, which are introduced in the paper. Our description is particularly detailed over fields of cohomological dimension at most two, and is related to quaternion algebras and the Brauer group. We then extend the results to certain rational function fields over real closed fields via Pfister's theory of quadratic forms and his solution to Hilbert's Seventeenth Problem.
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| 9. |
- Altafi, Nasrin, et al.
(författare)
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Complete intersection Jordan types in height two
- 2020
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Ingår i: Journal of Algebra. - : Academic Press. - 0021-8693 .- 1090-266X. ; 557, s. 224-277
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Tidskriftsartikel (refereegranskat)abstract
- We determine every Jordan type partition that occurs as the Jordan block decomposition for the multiplication map by a linear form in a height two homogeneous complete intersection (CI) Artinian algebra A over an algebraically closed field k of characteristic zero or large enough. We show that these CI Jordan type partitions are those satisfying specific numerical conditions; also, given the Hilbert function H(A), they are completely determined by which higher Hessians of A vanish at the point corresponding to the linear form. We also show new combinatorial results about such partitions, and in particular we give ways to construct them from a branch label or hook code, showing how branches are attached to a fundamental triangle to form the Ferrers diagram.
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| 10. |
- Altafi, Nasrin, et al.
(författare)
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The weak Lefschetz property of equigenerated monomial ideals
- 2020
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Ingår i: Journal of Algebra. - : Academic Press. - 0021-8693 .- 1090-266X. ; 556, s. 136-168
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Tidskriftsartikel (refereegranskat)abstract
- We determine a sharp lower bound for the Hilbert function in degree d of a monomial algebra failing the weak Lefschetz property over a polynomial ring with n variables and generated in degree d, for any d≥2 and n≥3. We consider artinian ideals in the polynomial ring with n variables generated by homogeneous polynomials of degree d invariant under an action of the cyclic group Z/dZ, for any n≥3 and any d≥2. We give a complete classification of such ideals in terms of the weak Lefschetz property depending on the action.
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