Dade, E. C. and Taussky, O. and Zassenhaus, H. (1962) On the theory of orders, in particular on the semigroup of ideal classes and genera of an order in an algebraic number field. Mathematische Annalen, 148 (1). pp. 31-64. ISSN 0025-5831. doi:10.1007/bf01438389. https://resolver.caltech.edu/CaltechAUTHORS:20201022-100905016
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Abstract
The study of fractional ideals of orders of algebraic number fields and their equivalence is closely related to the study of matrices with rational integral elements and their similarities under unimodular transformations. Such a study should at some stage proceed to the inspection of actual numerical examples. However, quite simple questions, such as the problem of the arithmetical equivalence of two ideals with the same order (see below), require a large number of computational steps. Therefore this task calls for the use of automatic highspeed computers.
| Item Type: | Article | |||||||||
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| Additional Information: | © 1962 Springer. (Received December 18, 1961) This work was supported in part by the Office of Naval Research at the California Institute of Technology and by the National Science Foundation at the California Institute of Technology (including the 1960 Group Theory Institute) and at the University of Notre Dame (1961 Symposium on Number Theory and Algebraic Geometry). | |||||||||
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| Issue or Number: | 1 | |||||||||
| DOI: | 10.1007/bf01438389 | |||||||||
| Record Number: | CaltechAUTHORS:20201022-100905016 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20201022-100905016 | |||||||||
| Official Citation: | Dade, E.C., Taussky, O. & Zassenhaus, H. On the theory of orders, in particular on the semigroup of ideal classes and genera of an order in an algebraic number field. Math. Ann. 148, 31–64 (1962). https://doi.org/10.1007/BF01438389 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 106213 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | George Porter | |||||||||
| Deposited On: | 22 Oct 2020 22:40 | |||||||||
| Last Modified: | 16 Nov 2021 18:51 |
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