Computational Commutative And Non-commutative Algebraic Geometry

✍ Scribed by Svetlana Cojocaru, Svetlana Cojocaru, Gerhard Pfister, Victor Ufnarovski

• Publisher: IOS Press
• Year: 2005
• Tongue: English
• Leaves: 336
• Series: NATO Science Series: Computer & Systems Sciences
• Edition: illustrated edition
• Category: Library

✦ Synopsis

This publication gives a good insight in the interplay between commutative and non-commutative algebraic geometry. The theoretical and computational aspects are the central theme in this study. The topic is looked at from different perspectives in over 20 lecture reports. It emphasizes the current trends in Commutative and Non-Commutative Algebraic Geometry and Algebra. The contributors to this publication present the most recent and state-of-the-art progresses which reflect the topic discussed in this publication. Both researchers and graduate students will find this book a good source of information on commutative and non-commutative algebraic geometry.

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✦ Table of Contents

Title page......Page 1
Preface......Page 5
Contents......Page 7
Noncommutative Algebraic Geometry and Algebra......Page 9
The Structure of Simp<infty (A) for Finitely Generated k-algebras A1......Page 11
On Preimages of Ideals in Certain Non-commutative Algebras......Page 52
Commutative Algebraic Geometry and Algebra......Page 71
Maximal Cohen-Macaulay Modules and Stable Vector Bundles......Page 73
On the Contact with the Polar......Page 82
On Some Generalization of Schubert's Varieties......Page 87
Lifting an Ideal from a Tight Bourbaki Sequence and Maximal Cohen-Macaulay Modules......Page 98
Some Applications of Resolution of Singularities from the Practical Point of View......Page 112
Finite Free Resolutions......Page 126
Computing the Integral Closure of an Ideal Using its Rees Algebra......Page 153
Modular Strata of Deformation Functors......Page 164
Algebraic Dependence of Polynomials After O. Perron and Some Applications......Page 175
A Remark on MCM-modules of Rank One Over a Smooth Plane Cubic......Page 182
Computer Algebra......Page 191
Problems in Interaction with the Computer Algebra System BERGMAN......Page 193
Involutive Algorithms for Computing Grobner Bases......Page 207
Idealization of Modules in Computer Algebra......Page 234
Algorithmic Problems in SAGBI Basis Calculations......Page 252
Topology and Differential Equations......Page 257
On Group Topologies on an Abelian Group Preceding One Another......Page 259
Commutative and Non-Commutative Algebras in the Study of Differential Equations......Page 276
Projective Planes and Quasigroups......Page 295
About the Description of All Projective Planes of the Prime Power Order......Page 297
On Simple n-ary Medial Quasigroups......Page 313
Author Index......Page 333