| 1. |
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| 2. |
- Boij, Mats, 1969-
(author)
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Betti numbers of compressed level algebras
- 1999
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In: Journal of Pure and Applied Algebra. - 0022-4049 .- 1873-1376. ; 134:2, s. 111-131
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Journal article (peer-reviewed)abstract
- We present a conjecture on the generic Betti numbers of level algebras. We prove the conjecture in the case of Gorenstein Artin algebras of embedding dimension four, and in the case of Artin level algebras whose socle dimension is large. Furthermore, we present computational evidence for the conjecture.
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| 3. |
- Boij, Mats, 1969-
(author)
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Components of the space parametrizing graded Gorenstein Artin algebras with a given Hilbert function
- 1999
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In: Pacific Journal of Mathematics. - : Mathematical Sciences Publishers. - 0030-8730 .- 1945-5844. ; 187:1, s. 1-11
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Journal article (peer-reviewed)abstract
- We give geometric constructions of families of graded Gorenstein Artin algebras, some of which span a component of the space Gor(T) parametrizing Gorenstein Artin algebras with a given Hilbert function T. This gives a lot of examples where Gor(T) is reducible. We also show that the Hilbert function of a codimension four Gorenstein Artin algebra can have an arbitrarily long constant part without having the weak Lefschetz property.
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| 4. |
- Boij, Mats
(author)
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Gorenstein algebras with nonunimodal Betti numbers
- 1999
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In: Mathematica Scandinavica. - : Det Kgl. Bibliotek/Royal Danish Library. - 0025-5521 .- 1903-1807. ; 84:2, s. 161-164
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Journal article (peer-reviewed)abstract
- We show the existence of graded Gorenstein algebras whose Betti numbers are not unimodal, contradicting a conjecture by R. Stanley. In fact, we prove that the Betti numbers given by the natural lower bound are non-unimodal in sufficiently high embedding dimension - greater than or equal to nine - and we have calculated two examples where the Betti numbers attain this lower bound.
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| 5. |
- Boij, Mats, 1969-
(author)
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Nonunimodality of graded Gorenstein Artin algebras
- 1994
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In: Proceedings of the American Mathematical Society. - 0002-9939 .- 1088-6826. ; 120:4, s. 1083-1092
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Journal article (peer-reviewed)abstract
- We give an explicit expression for the Hilbert function of a large class of graded Gorenstein Artin algebras and give a criterion for this function to be unimodal. As a result we obtain an abundance of graded Gorenstein Artin algebras with nonunimodal Hilbert function.
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| 6. |
- Normann, Dag, et al.
(author)
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Hyperfinite type structures
- 1999
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In: JOURNAL OF SYMBOLIC LOGIC. - : ASSN SYMBOLIC LOGIC INC. ; 64:3, s. 1216-1242
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Journal article (peer-reviewed)
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| 7. |
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| 8. |
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| 9. |
- Stoltenberg-Hansen, Viggo, et al.
(author)
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Computable rings and fields
- 1999
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In: Handbook of Computability Theory. - : Elsevier, Amsterdam. - 0444898824 ; , s. 363-447
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Book chapter (peer-reviewed)
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| 10. |
- Stoltenberg-Hansen, Viggo, et al.
(author)
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Effective algebras
- 1995
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In: Handbook of Logic in Computer Science, vol. 4. - : Oxford University Press, Oxford. - 0198537808 ; , s. 357-526
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Book chapter (pop. science, debate, etc.)
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