Some facts concerning integral representations of the ideals in an algebraic number field
This paper studies the application of ideal matrices [the author, Arch. Math. 13, 275--282 (1962; Zbl 0118.27504)] in a regular representation of the maximal order of an algebraic number field \(F\). By a theorem of \textit{C. C. MacDuffee} [Math. Ann. 105, 663--665 (1931; Zbl 0003.10005)] the ideal matrix of an ideal is the right (or left) gcd of the maps of the elements in the ideal. This matrix is determined up to a unimodular matrix factor. If it lies inside the map of the ideal then we have a principal ideal. If it does not lie inside for any unimodular factor (on the appropriate side) then it does not commute with all the maps of the ideal. Further discussions of the ideal matrix are included.
scientific article; zbMATH DE number 3676012