A Singular Introduction to Commutative Algebra [Hardcover]

Gert-Martin Greuel (Author), Gerhard Pfister (Author), O. Bachmann (Contributor), C. Lossen (Contributor), H. Schönemann (Contributor)

Book Description

Publication Date: December 4, 2007 | ISBN-10: 3540735410 | ISBN-13: 978-3540735410 | Edition: 2nd ed. 2008

This substantially enlarged second edition aims to lead a further stage in the computational revolution in commutative algebra. This is the first handbook/tutorial to extensively deal with SINGULAR. Among the book’s most distinctive features is a new, completely unified treatment of the global and local theories. Another feature of the book is its breadth of coverage of theoretical topics in the portions of commutative algebra closest to algebraic geometry, with algorithmic treatments of almost every topic.

Editorial Reviews

Review

Aus den Rezensionen zur 2. Auflage: "… Das ... Buch führt in die Kommutative Algebra ... so weit ein, wie das zum Verständnis der in SINGULAR verwendeten Begriffe ... nötig ist. ... Alle Begriffe ... und Konzepte werden ... durch … gerechnete Beispiele verdeutlicht. Beim Lesen hat man das angenehme Gefühl, dass das Buch viel an Inhalt vermittelt, dabei aber immer im positiven Sinn ‘am Boden bleibt‘. … Anhang A liefert den geometrischen Hintergrund für die ... Begriffe und Resultate der kommutativen Algebra. Dieser Abschnitt ist eine sehr konkrete und anschauliche Einführung in die algebraische Geometrie …" (Franz Pauer, in: Computeralgebra, Okt. 2008, Issue 43, S. 36 f.)   "... ein … Lehrbuch über kommutative Algebra ... Zunächst etwas mehr Aufwand, weil er neben Buch, Stift und Papier auch noch einen Computer benötigt, auf dem dann auch noch ein Programm installiert werden muss. Hier helfen die Autoren aber durch die Bereitstellung einer wunderbaren CD und nehmen dem Leser damit fast alle Schwierigkeiten ab … Danach hat man ... einen treuen Begleiter bei der Lektüre des Buches. ... Man kann also sofort seiner Neugier folgen, und das Lernen geschieht dann ganz nebenbei ..." (Klaus Altmann, in: Jahresbericht der Deutschen Mathematiker-Vereinigung, September/2009, Vol. 111, Issue 3, S. 33 ff.)

From the Back Cover

From the reviews: "…It is certainly no exaggeration to say that Greuel and Pfister's A Singular Introduction to Commutative Algebra aims to lead a further stage in the computational revolution in commutative algebra, in which computational methods and results become central to how the subject is taught and learned. […] Among the great strengths and most distinctive features of Greuel and Pfister's book is a new, completely unified treatment of the global and local theories. The realization that the two cases could be combined to this extent was decisive in the design of the Singular system, making it one of the most flexible and most efficient systems of its type. The authors present the first systematic development of this unified approach in a textbook here, and this aspect alone is almost worth the price of admission. Another distinctive feature of this book is the degree of integration of explicit computational examples into the flow of the text. Strictly mathematical components of the development (often quite terse and written in a formal "theorem-proof" style) are interspersed with parallel discussions of features of Singular and numerous Singular examples giving input commands, some extended programs in the Singular language, and output. […] Yet another strength of Greuel and Pfister's book is its breadth of coverage of theoretical topics in the portions of commutative algebra closest to algebraic geometry, with algorithmic treatments of almost every topic. A synopsis of the table of contents will make this clear. […] Greuel and Pfister have written a distinctive an highly useful book that should be in the library of every commutative algebrais and algebraic geometer, expert and novice alike. I hope that it achieves the educational impact it deserves." John B. Little, Monthly of The Mathematical Association of America, March 2004 "... The authors' most important new focus is the presentation of non-well orderings that allow them the computational approach for local commutative algebra. The accompanying CD-ROM also contains all the examples of the book. ... In fact the book provides an introduction to commutative algebra from a computational point of view. So it might be helpful for students and other interested readers (familiar with computers) to explore the beauties and difficulties of commutative algebra by computational experiences. In this respect the book is the one of the first samples of a new kind of textbooks in algebra." P.Schenzel, Zentralblatt für Mathematik 1023.13001, 2003

Product Details

• Hardcover: 710 pages
• Publisher: Springer; 2nd ed. 2008 edition (December 4, 2007)
• Language: English
• ISBN-10: 3540735410
• ISBN-13: 978-3540735410
• Product Dimensions: 9.4 x 6.5 x 1.7 inches
• Shipping Weight: 2.6 pounds (View shipping rates and policies)
• Amazon Best Sellers Rank: #1,886,720 in Books (See Top 100 in Books)