Preface Introduction Conventions and terminology 1. Commutative rings and modules 2. prime ideals 3. Properties of extension rings 4. Valuation rings 5. Dimension theory 6. Regular sequences 7. Regular rings 8. Flatness revisited 9. Derivations 10. I-smoothness 11. Applications of complete local rings Appendices References Index.

Commutative Ring Theory

羟氨苄青霉素引起大疱性类天疱疮样疹

https://www-polsys.lip6.fr/~jcf/Papers/F99a.pdf

A new efficient algorithm for computing Gröbner bases (F4)

From the reviews of the first edition: "It is certainly no exaggeration to say that A Singular Introduction to Commutative Algebra aims to lead a further stage in the computational revolution in commutative algebra . Among the great strengths and most distinctive features is a new, completely unified treatment of the global and local theories. making it one of the most flexible and most efficient systems of its type....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....Greuel and Pfister have written a distinctive and highly useful book that should be in the library of every commutative algebraist and algebraic geometer, expert and novice alike." J.B. Little, MAA, March 2004 The second edition is substantially enlarged by a chapter on Groebner bases in non-commtative rings, a chapter on characteristic and triangular sets with applications to primary decomposition and polynomial solving and an appendix on polynomial factorization including factorization over algebraic field extensions and absolute factorization, in the uni- and multivariate case.

A Singular Introduction to Commutative Algebra

Polynomials in one variable Grobner bases of zero-dimensional ideals Bernstein's theorem and fewnomials Resultants Primary decomposition Polynomial systems in economics Sums of squares Polynomial systems in statistics Tropical algebraic geometry Linear partial differential equations with constant coefficients Bibliography Index.

/pdf/solving-systems-of-polynomial-equations-3xfr3xgaue.pdf

Solving systems of polynomial equations

This is a book about Grbner 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. This is academic teaching at its best;" (H.Stetter, IMN 2003) "Every paragraph of the book shows how much the authors have enjoyed translating into printed matter the outcome of a long, large, deep and personal relation with computationally oriented commutative algebra." (L.Gonzlez-Vega and T.Recio, ACM SIGSAM Bull. 2004) "Each section begins with a quotation and an overview in which "Italian imagination overtakes German rigor". These introductions and the following main bodies of each section are well written, engaging and often amusing. The book is a pleasure to read." (J.Little, Math. Reviews 2001)

Computational Commutative Algebra 1

The Gröbner fan of an ideal

Term Orderings on the Polynominal Ring

In this paper redescribe some experimentti findings on selection strategies for Gr6bner basis computation with the Buchberger algorithm. In particular, the results suggest that the “sugar flavor” of the “normal selection”, implemented first in COCOA, then in AlPI, [14], [15] (up to now in the muLISP version, in a short time in the COMMON-LISP version, including the parallel version, [1]) and now in SCRATCHPAD-II, is the best choice for a selection strategy. It has to be combined with the “straightforward” simplification strategy and with a special form of the Gebauer-Moller criteria to obtain the best results. The idea of the “sugar flavor” is the following: the Buchberger algorithm for homogeneous ideals, with degreecompatible term ordering and normal selection strategy, usually works fine. Homogenizing the basis of the ideal is good for the strategy, but bad for the basis to be computed. The sugar flavor computes, for every polynomial in the course of the algorithm, ‘(the degree that it would have if computed with the homogeneous algorithm”, and uses this phantom degree (the sugar) only for the selection strategy. We have tested several examples with different selection strategies, and the sugar flavor has proved to be always the best choice or very near to it. The comparison between the different variants of the sugar flavor has been made, but the results are up to now inconclusive. We include a complete deterministic description of the Buchberger algorithm as it was used in our experiments.l

Lorenzo Robbiano

Papers

Computational Commutative Algebra 1

The Gröbner fan of an ideal

Term Orderings on the Polynominal Ring

“One sugar cube, please” or selection strategies in the Buchberger algorithm

On the theory of graded structures