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A class of finite commutative rings constructed from Witt rings

  • Thomas Craven (a1) and Monika Vo (a2)
Abstract

Motivated by constructions of Witt rings in the algebraic theory of quadratic forms, the authors construct new classes of finite commutative rings and explore some of their properties. These rings are constructed as quotient rings of a special class of integral group rings for which the group is an elementary 2-group. The new constructions are compared to other rings in the literature.

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[2]T. Craven , ‘Stability in Witt rings’, Trans. Amer. Math. Soc. 225 (1977), 227242.

[3]T. Craven , ‘Characterizing reduced Witt rings of fields’, J. Algebra 53 (1978), 6877.

[4]T. Craven , ‘Fields maximal with respect to a set of orderings’, J. Algebra 115 (1988), 200218.

[5]R. Elman , T.Y. Lam and A.R. Wadsworth , ‘Pfister ideals in Witt rings‘, Math. Ann. 245 (1979), 219245.

[6]R. Fitzgerald and J. Yucas , ‘Combinatorial techniques and abstract Witt rings, II’, Rocky Mountain J. Math. 19 (1989), 687708.

[7]J. Kleinstein and A. Rosenberg , ‘Signatures and semisignatures of abstract Witt rings and Witt rings of semilocal rings’, Canadian J. Math. 30 (1978), 872895.

[8]M. Knebusch , A. Rosenberg and R. Ware , ‘Structure of Witt rings and quotients of abelian group rings’, American J. Math. 94 (1972), 119155.

[9]M. Knebusch , A. Rosenberg and R. Ware , ‘Signatures on semilocal rings’, J. Algebra 26 (1973), 208250.

[11]T.Y. Lam , Orderings, valuations and quadratic forms, CBMS Regional Conference Series in Mathematics 52 (Amer. Math. Soc., Providence, RI, 1983).

[14]M. Marshall , ‘The Witt ring of a space of orderings’, Trans. Amer. Math. Soc. 258 (1980), 505521.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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