La théorie géométrique des diviseurs élémentaires d’après M. Krull. (Russian. French summary) Zbl 0015.00104

Trav. Univ. Odessa, Math. 1, 89-108 (1935).
The author follows the ideas of Krull’s papers on abelian groups [Math. Z. 23, 161–196 (1925; JFM 51.0116.03); Sitzungsber. Heidelb. Akad. Wiss. 1926, No. 1, 32 S. (1926; JFM 52.0111.02)] and develops, in a geometrical language, the theory of elementary divisors for an arbitrary number field. With the aid of some simple geometrical concepts he establishes the fundamental theorems for a decomposition of vector space into cyclic subspaces, which enable him to obtain easily the canonical forms for a matrix, and some other well-known results of matrix theory.
For other closely related work see: M. H. Ingraham [Bull. Am. Math. Soc. 39, 379–382 (1933; Zbl 0007.05105; JFM 59.0904.03); M. H. Ingraham and M. C. Wolf [ibid. 42, 493 (1936; JFM 62.0062.08)] and N. Jacobson [Proc. Natl. Acad. Sci. USA 21, 667–670 (1935; Zbl 0013.14603; JFM 61.0993.03)].


12E99 General field theory
15A21 Canonical forms, reductions, classification