Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-25T07:17:02.240Z Has data issue: false hasContentIssue false
  • English
  • Français

Gorenstein Witt Rings II

Published online by Cambridge University Press:  20 November 2018

Robert W. Fitzgerald
Robert W. Fitzgerald*
Affiliation:
Southern Illinois University, Carbondale, IL, USA 62901-4408 e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The abstract Witt rings which are Gorenstein have been classified when the dimension is one and the classification problem for those of dimension zero has been reduced to the case of socle degree three. Here we classify the Gorenstein Witt rings of fields with dimension zero and socle degree three. They are of elementary type.

Keywords

11E8113H10
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 3 , 01 June 1997 , pp. 499 - 519
Copyright
Copyright © Canadian Mathematical Society 1997

References

1. Cordes, C. and Ramsey, J., Quadratic forms over fields with u = q, /2 < +∞, Fund. Math. 99(1978), 1–10.Google Scholar
2. Elman, R. and Lam, T.-Y., Classification theorems for quadratic forms over fields, Math. Helv. 49(1974), 373–381.Google Scholar
3. Elman, R., Lam, T.-Y. and Wadsworth, A., Amenable fields and Pfister extensions, Conference on quadratic forms 1976, Queen's papers in pure and applied math. No. 46, 1977. 445–491.Google Scholar
4. Elman, R., Pfister ideals in Witt rings, Math. Ann. 245(1979), 219–245.Google Scholar
5. Fitzgerald, R., Gorenstein Witt rings, Canad. J. Math. 40(1988), 1186–1202.Google Scholar
6. Fitzgerald, R., Local artinian rings and the Fröberg relation, Rocky Mtn. J. Math., to appear.Google Scholar
7. Fitzgerald, R., Bass series of small Witt rings, preprint.Google Scholar
8. Fitzgerald, R. and Yucas, J., Combinatorial techniques and abstract Witt rings I, J. Algebra 114(1988), 40–52.Google Scholar
9. Lam, T.-Y., The Algebraic Theory of Quadratic Forms, Benjamin, Reading, Mass., 1973.Google Scholar
10. Kula, M., Finitely Generated Witt Rings, Univwersytet Ślaski, Katowice, 1991.Google Scholar
11. Marshall, M., Abstract Witt rings, Queen's papers in pure and applied math. No. 57, Queen's University, Kingston, Ontario, 1980.Google Scholar
12. Szczepanik, L., Quadratic forms schemes with non-trivial radical, . Colloq. Math. 49(1985), 143–160.Google Scholar
13. Szymiczek, K., Generalized Hilbert fields, J. Reine Angew. Math. 329(1981), 58–65.Google Scholar