Ideal matrices. I

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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