By Nicolas Bourbaki

ISBN-10: 2705612610

ISBN-13: 9782705612610

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Read Online or Download Algebre, Chapitre 8: Modules et anneaux semi-simples (Elements de mathematique, Fascicule 23, ASI 1261) PDF

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Extra resources for Algebre, Chapitre 8: Modules et anneaux semi-simples (Elements de mathematique, Fascicule 23, ASI 1261)

Example text

So erscheint z. B. das, was fUr den SchUler ein anschaulicher Satz tiber das Erweitern bzw. Kurzen der Bruche ist, hier in der Gestalt einer Definition der Gleichheit: Zwei Bruche ~, Jheif3en gleich, wenn a d = b c ist. Ahnlich wird das Grof3er und Kleiner definiert, ahnlich wird . a c ad+bc festgesetzt, daB als Summe zwezer Bruche b' d der Bruch bd be- zeichnet werden mage usw. Dann wird bewiesen, daB die so definierten Operationen in dem neu entstandenen Zahlenkreise formal genau die Eigenschaften der Addition und Multiplikation fUr ganze Zahlen besitzen, d.

Getreten. Mit der Raumanschauung nun liegt es ahnlich: Betrachten wir z. B. den Abstand zweier Punkte, so konnen wir ihn nur mit einer gewissen beschriinkten Genauigkeit abschatzen und messen, denn unser Auge kann Strecken, deren Unterschied unter einer gewissen Grenze liegt, nicht mehr als verschieden auffassen; das ist die Tatsache der Schwelle, die in der ganzen Psychologie eine so groBe Rolle spielt. Diese Erscheinung bleibt dem Wesen nach auch bestehen. wenn wir unser Auge durch die denkbar scharfsten Hilfsmittel unterstiitzen; denn es gibt physikalische Eigenschaften, die einen gewissen Genauigkeitsgrad zu iiberschreiten nicht gestatten.

Deuten wir die Zahlen auf der Abszissenachse und bemerken, daB die Strecke zwischen den Punkten b und a die Lange a - b I o I I b'-v-"a a-b I c hat, so lehrt ein Blick auf die obige Abbildung: Zieht man von c die Strecke a - b ab, so erhalt man dasselbe, wie wenn man erst die ganze Strecke a abzieht und dann den Teil b wieder hinzufiigt, d. : (1) c - (a - b) = c - a + b. 2. Es sei a> b und c> d; dann sind auch a - b und c - d positive ganze Zahlen. Wir wollen das Produkt (a - b) . (c - d) untersuchen; dazu zeichnen wir uns das in Abb.

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Algebre, Chapitre 8: Modules et anneaux semi-simples (Elements de mathematique, Fascicule 23, ASI 1261) by Nicolas Bourbaki


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