| 1. |
- Kantor, Isaiah, et al.
(författare)
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Ring-theoretic properties of commutative algebras of invariants
- 2003
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Ingår i: Journal of Algebra. - 0021-8693. ; 266:1, s. 239-260
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Tidskriftsartikel (refereegranskat)abstract
- The commutative algebra of invariants of a Lie super-algebra need not be affine, but does have a common ideal with an affine algebra, in all the known examples. This leads us to extend a class of algebras C to a class which we call "nearly C", by admitting those algebras C having a common ideal A with an algebra (containing C) in C such that C/A is an element of C. We generalize this notion slightly. study the prime ideals of such algebras, and extend some of the standard theorems about affine algebras, Noetherian rings, and Dedekind domains. Our main theorem is that nearly affine domains are catenary, and the Krull dimension equals the transcendence degree of the quotient field. Nevertheless, it is known that nearly affine domains need not be Mori. (C) 2003 Elsevier Inc. All rights reserved.
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| 2. |
- 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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| 3. |
- 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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| 4. |
- 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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| 5. |
- 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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| 6. |
- 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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| 7. |
- Alfes, Claudia, et al.
(författare)
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A classification of polyharmonic Maaß forms via quiver representations
- 2025
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Ingår i: Journal of Algebra. - 0021-8693 .- 1090-266X. ; 661, s. 713-756
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Tidskriftsartikel (refereegranskat)abstract
- We give a classification of the Harish-Chandra modules generated by the pullback to SL2(R) of polyharmonic Maaß forms for congruence subgroups of SL2(Z) with exponential growth allowed at the cusps. This extends results of Bringmann–Kudla in the harmonic case. While in the harmonic setting there are nine cases, our classification comprises ten; A new case arises in weights k>1. To obtain the classification we introduce quiver representations into the topic and show that those associated with polyharmonic Maaß forms are cyclic, indecomposable representations of the two-cyclic or the Gelfand quiver. A classification of these transfers to a classification of polyharmonic weak Maaß forms. To realize all possible cases of Harish-Chandra modules we develop a theory of weight shifts for Taylor coefficients of vector-valued spectral families. We provide a comprehensive computer implementation of this theory, which allows us to provide explicit examples.
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| 8. |
- 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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| 9. |
- 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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| 10. |
- Alsaody, Seidon
(författare)
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Groups of type E6 and E7 over rings via Brown algebras and related torsors
- 2024
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Ingår i: Journal of Algebra. - : Elsevier. - 0021-8693 .- 1090-266X. ; 656, s. 24-46
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Tidskriftsartikel (refereegranskat)abstract
- We study structurable algebras and their associated Freudenthal triple systems over commutative rings. The automorphism groups of these triple systems are exceptional groups of type E 7 , and we realize groups of type E 6 as centralizers. When 6 is invertible, we further give a geometric description of homogeneous spaces of type E 7 / E 6 , and show that they parametrize principal isotopes of Brown algebras. As opposed to the situation over fields, we show that such isotopes may be non-isomorphic. (c) 2023 The Author. Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).
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