Pacific Journal of Mathematics

Witt rings under odd degree extensions.

Robert W. Fitzgerald

Article information

Source
Pacific J. Math., Volume 158, Number 1 (1993), 121-143.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102634612

Mathematical Reviews number (MathSciNet)
MR1200831

Zentralblatt MATH identifier
0790.11034

Subjects
Primary: 11E81: Algebraic theory of quadratic forms; Witt groups and rings [See also 19G12, 19G24]
Secondary: 12D15: Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) [See also 11Exx]

Citation

Fitzgerald, Robert W. Witt rings under odd degree extensions. Pacific J. Math. 158 (1993), no. 1, 121--143. https://projecteuclid.org/euclid.pjm/1102634612


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References

  • [I] H. Bass, O Ae ubiquity of Gorenstein rings, Math. Z., 82 (1963), 8-28.
  • [2] A. Carson and M. Marshall, Decomposition of Witt rings, Canad. J. Math., 34 (1982), 1276-1302.
  • [3] P. Dutton, Prime ideals attached to a module, Quart. J. Math. (2), 29 (1978), 403-413.
  • [4] R. Elman and T.-Y. Lam, Quadraticforms overformally real fields andpythago- rean fields, Amer. J. Math., 94 (1972), 1155-1194.
  • [5] R. Elman and T.-Y. Lam, Quadratic forms under algebraicextensions, Math. Ann., 219 (1976), 21-
  • [6] R. Elman, T.-Y. Lam, and A. Wadsworth, Orderings under field extensions, J. Reine Angew. Math., 306 (1979), 7-27.
  • [7] C. Faith, Algebra: Rings, Modules and CategoriesI, Grundlehren Math. Wiss., vol. 190, Springer-Verlag, New York/Heidelberg/Berlin, 1973.
  • [8] R. Fitzgerald, Primary ideals in Witt rings,J. Algebra, 96 (1985), 368-385.
  • [9] R. Fitzgerald, Gorenstein Witt rings, Canad. J. Math., 60 (1988), 1186-1202.
  • [10] J. Iroz and D. Rush, Associatedprime ideals in non-noetheranrings, Canad. J. Math., 36 (1984), 344-360.
  • [II] T.-Y. Lam, The Algebraic Theory of Quadratic Forms, Benjamin, Reading, Mass., 1980.
  • [12] M. Marshall, Abstract Witt rings, Queen's Papers in Pure and Appl. Math., vol.
  • [57] Kingston, Ont., 1980.
  • [13] D. G. Northcott,Remarks on the theory of attachedprime ideals,Quart. J. Math. (2), 33(1982), 239-245.
  • [14] J.-P. Serre, Local Fields, Graduate Texts in Math., vol. 67, Springer-Verlag, New York/Heidelberg/Berlin,1979.
  • [15] W. Scharlau, Quadratic and Hermitian Forms, Grundlehren Math. Wiss., vol. 270, Springer-Verlag, Berlin/Heidelberg/New York/Tokyo, 1985.
  • [16] R. Ware, Automorphisms of Pythagorean fields and their Witt rings, Comm. Algebra 17 (4) (1989), 945-969.