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Ideal matrices. I

Taussky, Olga (1962) Ideal matrices. I. Archiv der Mathematik, 13 (1). pp. 275-282. ISSN 0003-889X. doi:10.1007/bf01650074.

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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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Official Citation:Taussky, O. Ideal matrices. I. Arch. Math 13, 275–282 (1962).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:106212
Deposited By: George Porter
Deposited On:22 Oct 2020 22:36
Last Modified:16 Nov 2021 18:51

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