Grobner bases : a computational approach to commutative algebra / Thomas Becker, Volker Weispfenning ; Heinz Kredel

The thoroughness of the book should make it an excellent reference guide to Gröbner bases and their application, and it also is very suitable for an introduction to Gröbner bases for researchers or students with some prior commutative algebra knowledge. It may also be used by computer algebra users who wish to investigate the correctness of various algorithms and approaches. Although the book covers much of the second year commutative algebra curriculum, I however judge it less apt for replacing ordinary such courses, not so much in view of its formalism, but because the concentration on Gröbner bases makes the authors skip some issues and shift emphasis on others. The computational approach is naturally much more dependent on presentations of algebraic objects, and in this book the "intrinsicity'' (independence up to isomorphisms) of various properties and invariants (e.g., the Krull dimension) is played down. In spite of some interesting examples, the book is not quite successful in exhibiting Gröbner bases as a "cornerstone of commutative algebra''. (MathSciNet)

Bibliogr. p. 531-559. Index