INTRODUCING THE NOTION "LATTICE" (DUALGRUPPE).

DEDEKIND, RICHARD.

Ueber die von drei Moduln erzeugte Dualgruppe.

Leipzig, B.G. Teubner, 1900. Orig. printed wrappers, no backstrip. In "Mathematische Annalen. Gegenwärtig hrsg. von Felix Klein, Walter Dyck, Adolph Mayer. 53. Band, 3. Heft, 1900." Pp. (289-)464. The whole issue (Heft 3) present with wrappers. Dedekind's paper: pp. 371-403.

First edition and first appearance in print of a fundamental paper in "Lattice-Theory".
"dedekind's number-theoretic investigations led to the introduction of the notion of a "lattice" (under the name "Dualgruppe"), at first implicitly and then explicitly. Dedekind studied the notion further, as a topic in itself, in two relatively lates articles:"eber Zerlegungen von Zahlen durch ihrer grössten gemeinsamen Teiler" (1897) and "Über die von drei Moduln erzeugte Dualgruppe" (1900). (The paper offered). And while these articles did not have the same immediate and strong impact that several of his other works had, they were subsequently recognized as original, systematic contributions to lattice theory, especially the study of modular lattices." (Stanford Encycl. of Philosophy).
This issue of Mathematische Annalen also contains the importen memoir by MAX DEHN: "Die Legendre'schen Sätze über die Winkelsumme im Dreieck.", pp. 404-39, in which he proves that there is a geometry in which the angle sum is two right angles, similar but noncongruent triangles exist, and an infinity of straight lines that are paralell to a given line may be drawn through a given point. Sommerville: Bibliography of Non-Euclidean Geometry: 1900:1).

Order-nr.: 41241