Originally published by Van Nostrand Publishing Company ...

Dieses Buch ist aus einer Reihe von Vorlesungen an der Universität Bonn entstanden, die sich an Studierende im Hauptstudium wandte. Es beginnt mit einer Einführung in die homologische Algebra, die Garbentheorie und die Kohomologie von Garben. Darauf aufbauend kommt eine Einführung in die moderne algebraische Geometrie. ...

This is the softcover reprint of the English translation of 1972 (available from Springer since 1989) of the first 7 chapters of Bourbaki's 'Algèbre commutative'. It provides a very complete treatment of commutative algebra, enabling the reader to go further and study algebraic or arithmetic geometry. The first 3 chapters treat in succession the concepts of flatness, localization and completions (in the general setting of graduations and ...

This book is an attempt to write on commutative algebra in a way that includesthe geometric ideas that played a great role in its formation; with a view,in short, towards Algebraic Geometry. The author provides a book that coversthe material that graduate students studying Algebraic Geometry - and inparticular those studying the book Algebraic Geometry by Robin Hartshorne- should know. The reader should have had one year of basic graduate ...

This is a book about Gröbner bases and their applications. It contains 3 chapters, 20 sections, 44 tutorials, 165 exercises, and numerous further amusements. It is going to help you bridge the gap between theoretical computer algebra and actual computation. We hope you will have as much fun reading it as the authors had writing it!
From the reviews:
"This is one of the most refreshing mathematical books I have ever held in my hands. ...

The present book is devoted to a study of relative Prüfer rings and Manis valuations, with an eye to application in real and p-adic geometry. If one wants to expand on the usual algebraic geometry over a non-algebraically closed base field, e.g. a real closed field or p-adically closed field, one typically meets lots of valuation domains. Usually they are not discrete and hence not noetherian. Thus, for a further develomemt of real ...

This self-contained monograph is the first to feature the intersection of the structure theory of noncommutative associative algebras and the algorithmic aspect of Groebner basis theory. A double filtered-graded transfer of data in using noncommutative Groebner bases leads to effective exploitation of the solutions to several structural-computational problems, e.g., an algorithmic recognition of quadric solvable polynomial algebras, computation ...

Gröbner-Basen werden von Mathematikern und Informatikern zunehmend für eine breite Palette von Anwendungen genutzt, in denen die algorithmische algebraische Geometrie eine Rolle spielt. Hier werden Gröbner-Basen von einem konstruktiven, wenig abstrakten Standpunkt aus behandelt, wobei nur geringe Vorkenntnisse in linearer Algebra und komplexen Zahlen vorausgesetzt werden; zahlreiche Beispiele helfen bei der Durchdringung des ...

From the reviews: "... Many parts of the book can be read by anyone with a basic abstract algebra course... it was one of the author's intentions to equip students who are interested in computational problems with the necessary algebraic background in pure mathematics and to encourage them to do further research in commutative algebra and algebraic geometry. But researchers will also benefit from this exposition. They will find an up-to-date ...

Some remarkable connections between commutative algebra and combinatorics have been discovered in recent years. This book provides an overview of two of the main topics in this area. The first concerns the solutions of linear equations in nonnegative integers. Applications are given to the enumeration of integer stochastic matrices (or magic squares), the volume of polytopes, combinatorial reciprocity theorems, and related results. The second ...