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Extensions of self-dual orders

Published online by Cambridge University Press:  24 October 2008

Michael Singer
Michael Singer
Affiliation:
Chalmers University of Technology and University of Göteborg, Sweden
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Extract

We give a new criterion for an order in a commutative split algebra over the quotient field of a discrete valuation ring R to be self-dual. We derive a result on the ideal classes whose order is an extension by R of a self-dual order. This yields a wide generalization of a theorem of Faddeev(1). We can also answer a question arising from a paper of Fröhlich(2).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 70 , Issue 1 , July 1971 , pp. 5 - 7
Copyright
Copyright © Cambridge Philosophical Society 1971

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References

REFERENCES

(1)Faddeev, D. K.On the theory of cubic Z-rings. Trudy Mat. Inst. Steklov 80 (1965), 183–187Google Scholar
(2)Fröhlich, A.Invariants for modules over commutative separable orders. Quart. J. Math. Oxford (Ser. 2), 16 (1965), 193–232.CrossRefGoogle Scholar
(3)Singer, M.Invertible powers of ideals over orders in commutative separable algebras. Proc. Cambridge Philos. Soc. 67 (1970), 237–242.CrossRefGoogle Scholar
(4)Singer, M.A product theorem for ideals over orders. Proc. Cambridge Philos. Soc. 68 (1970), 17–20.CrossRefGoogle Scholar