Idealtheorie

Name: Idealtheorie
Brand: Springer
SKU: 9783642870347
Price: 3432.0 INR
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by Wolfgang Krull

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ISBN13: 9783642870347
Binding: Paperback
Subject: N/A
Publisher: Springer
Publisher Imprint: Springer
Publication Date: August 23, 2014
Pages: 160
Original Price: EUR 46.72
Language: German
Edition: 2. Aufl. 1968.
Item Weight: 254 grams
BISAC Subject(s): Algebra / General

About The Book

1. Grundlagen und Ausgangspunkte.- 1. Gruppen mit Operatoren und Ideale.- 2. Prim- und Primärideale. Polynomringe.- 3. Der Zerlegungssatz in abstrakten Ringen.- 4. Zahlentheoretische Grundlagen der Idealtheorie.- 5. Ganz abgeschlossene Integritätsbereiche.- 2. Abstrakte additive Idealtheorie.- 6. Isolierte Komponentenideale.- 7. Quotientenringe.- 8. Teilerfremde Ideale. Direkte Summen.- 9. Einartige Nullteilerringe.- 10. Einartige Integritätsbereiche.- 11. Operatorgruppen.- 12. Elementarteilergruppen.- 13. Primäre (Nullteiler-) Ringe.- 14. Additive Theorie der O-Ringe.- 15. Prim- und Primäridealketten in O-Ringen.- 3. Polynomringe.- 16. Integritätsbereiche von endlichem Transzendenzgrad.- 17. Endliche Integritätsbereiche und Polynomringe. Ungemischtheitssätze.- 18. Allgemeine und spezielle Nullstellen eines Polynomideals.- 19. Nullstellentheorie der Potenzreihenideale.- 20. Das Rechnen mit Polynomidealen.- 21. Gruppentheorie der Polynomideale.- 22. Eliminationstheorie.- 23. DerBézoutsche Satz und die Hentzeltschen Nullstellensätze.- 24. Hilberts Funktion.- 25. Das inverse System.- 26. Die Multiplizitätstheorie von vanderWaerden.- 27. Der Grad einer Mannigfaltigkeit und der allgemeine Bézoutsche Satz.- 28. Zweifach projektive Räume.- 4. Einartige Bereiche.- 29. Endliche algebraische Erweiterung primärer Ringe.- 30. Konstruktiver Aufbau primärer zerlegbarer Ringe.- 31. Die perfekten Hüllen der Integritätsbereiche mit Z.P.I.- 32. Erweiterung eines einartigen Integritätsbereichs zum ganz abgeschlossenen Ring.- 33. Normensätze.- 34. Diskriminantensätze.- 35. Verallgemeinerter Diskriminantensatz. Endlichkeitsprobleme.- 5. Bewertungstheorie.- 36. Bewertungsringe.- 37. Hauptordnungen.- 38. Z.P.E.-Ringe.- 39. Abschließung eines O-Rings.- 40. Allgemeine Bewertungsringe.- 41. Idealtheorie der Bewertungsringe.- 42. Bewertungen endlicher Erweiterungskörper eines Grundkörpers.- 6. V-Ideale und A-Ideale. Verhalten der Primideale bei Ringerweiterungen.- 43. V-Ideale.- 44. Unendliche algebraische Zahlkörper.- 45. Polynomringsätze und Permanenzsätze.- 46. Multiplikationsringe und A-Ideale.- 47. Einordnung des A-Prozesses in die Bewertungstheorie.- 48. Der Permanenzsatz der Primideale.- 49. Zusammenhang zwischen den Primidealen verschiedener Ringe mit gleichem Quotientenkörper.- 50. Divisoren zweiter Art.- Anhang: Bemerkungen zur Terminologie.- Ergänzungen zur 2. Auflage.

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