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Combinatorial and Computational Algebra
Edited by: Kai Yuen Chan, Alexander A. Mikhalev, Man-Keung Siu, and Jie-Tai Yu, University of Hong Kong, China, and Efim I. Zelmanov, Yale University, New Haven, CT

Contemporary Mathematics
2000; 305 pp; softcover
Volume: 264
ISBN-10: 0-8218-1984-4
ISBN-13: 978-0-8218-1984-5
List Price: US$87
Member Price: US$69.60
Order Code: CONM/264
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See also:

Symbolic Computation: Solving Equations in Algebra, Geometry, and Engineering - Edward L Green, Serkan Hosten, Reinhard C Laubenbacher and Victoria Ann Powers

Recent Advances in Scientific Computing and Partial Differential Equations - S Y Cheng, C-W Shu and T Tang

This volume presents articles based on the talks at the International Conference on Combinatorial and Computational Algebra held at the University of Hong Kong (China). The conference was part of the Algebra Program at the Institute of Mathematical Research and the Mathematics Department at the University of Hong Kong. Topics include recent developments in the following areas: combinatorial and computational aspects of group theory, combinatorial and computational aspects of associative and nonassociative algebras, automorphisms of polynomial algebras and the Jacobian conjecture, and combinatorics and coding theory.

This volume can serve as a solid introductory guide for advanced graduate students, as well as a rich and up-to-date reference source for contemporary researchers in the field.


Graduate students and research mathematicians interested in algebra and combinatorics.

Table of Contents

Combinatorial and computational aspects of group theory
  • E. Aljadeff and A. R. Magid -- Deformations and liftings of representations
  • A. Yu. Ol'shanskii and M. V. Sapir -- Embeddings of relatively free groups into finitely presented groups
  • A. Shalev -- Fixed point ratios, character ratios, and Cayley graphs
Combinatorial and computational aspects of associative and nonassociative algebras
  • L. A. Bokut, Y. Fong, and W.-F. Ke -- Gröbner-Shirshov bases and composition lemma for associative conformal algebras: An example
  • Y. Fong -- Derivations in near-ring theory
  • A. A. Mikhalev and J.-T. Yu -- Automorphic orbits of elements of free algebras with the Nielsen-Schreier property
  • A. V. Mikhalev and I. A. Pinchuk -- Universal central extensions of the matrix Lie superalgebras sl\((m,n,A)\)
  • G. F. Pilz -- The useful world of one-sided distributive systems
  • E. Zelmanov -- On the structure of conformal algebras
Automorphisms of polynomial algebras and the Jacobian conjecture
  • L. A. Campbell -- Unipotent Jacobian matrices and univalent maps
  • V. Drensky and J.-T. Yu -- Automorphisms and coordinates of polynomial algebras
  • A. van den Essen -- On Bass' inverse degree approach to the Jacobian conjecture and exponential automorphisms
  • A. van den Essen and P. van Rossum -- A note on possible counterexamples to the Abhyankar-Sathaye conjecture constructed by Shpilrain and Yu
  • W. D. Neumann and P. G. Wightwick -- Algorithms for polynomials in two variables
  • V. Shpilrain and J.-T. Yu -- Peak reduction technique in commutative algebra: A survey
  • D. Wright -- Reversion, trees, and the Jacobian conjecture
Combinatorics and coding theory
  • W.-C. W. Li -- Various constructions of good codes
  • M.-K. Siu -- Combinatorics and algebra: A medley of problems? A medley of techniques?
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