Taussky, Olga (1962) Ideal matrices. I. Archiv der Mathematik, 13 (1). pp. 275-282. ISSN 0003-889X. doi:10.1007/bf01650074. https://resolver.caltech.edu/CaltechAUTHORS:20201022-100904906
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Abstract
By an ideal matrix is understood a square matrix of rational integers which transforms a basis for the integers of an algebraic number field into a basis for an ideal in this ring. The same term will be used also for the analogous relation in an order of such a field. (This concept was studied by MACDUFFEE [1], for associative algebras over the rationals, later for abstract associative algebras [2]; it goes back to Poincaré [3], [4] and CHÂTELET [5]). In this note two aspects of ideal matrices are studied: 1) Ideal matrices and their connection with classes of matrices. 2) For what kind of number field is a given non-singular square matrix of rational integers an ideal matrix?
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| Additional Information: | © 1962 Springer. Eingegangen am 12. 2. 1962. To R. BAER on his sixtieth birthday. This work was carried out (in part) under a grant of National Science Foundation. Acknowledgement is made to helpful remarks by E. C. DADE. | |||||||||
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| Issue or Number: | 1 | |||||||||
| DOI: | 10.1007/bf01650074 | |||||||||
| Record Number: | CaltechAUTHORS:20201022-100904906 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20201022-100904906 | |||||||||
| Official Citation: | Taussky, O. Ideal matrices. I. Arch. Math 13, 275–282 (1962). https://doi.org/10.1007/BF01650074 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 106212 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | George Porter | |||||||||
| Deposited On: | 22 Oct 2020 22:36 | |||||||||
| Last Modified: | 16 Nov 2021 18:51 |
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