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An elementary proof of the invertible powers theorem

Published online by Cambridge University Press:  24 October 2008

Michael Singer
Affiliation:
Institute of Mathematics, The Hebrew University of Jerusalem, Israel

Extract

In this note we give a new, easy proof of the results on invertible powers of ideals that we established in (3). The deduction of the Dade–Taussky–Zassenhaus theorems (1) may be carried out as we did before in (3).

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

(1)Dade, E. C., Taussky, O. and Zassenhaus, H.On the theory of orders, in particular on the semigroups of ideal classes and genera of an order in an algebraic number field. Math. Ann. 148 (1962), 3164.CrossRefGoogle Scholar
(2)Fröhlich, A.Invariants for modules over commutative separable orders. Quart. J. Math. Oxford, Ser. 2, 16 (1965), 193232.CrossRefGoogle Scholar
(3)Singer, M.Invertible powers of ideals over orders in commutative separable algebras. Proc. Cambridge Philos. Soc. 67 (1970), 237242.CrossRefGoogle Scholar
(4)Singer, M.A product theorem for ideals over orders. Proc. Cambridge Philos. Soc. 68 (1970), 1720.CrossRefGoogle Scholar
(5)Singer, M.A product theorem for lattices over orders. Math. Scand. 29 (1971), 5054.CrossRefGoogle Scholar
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