Software

• Macaulay 2 is a software system devoted to supporting research in algebraic geometry and commutative algebra.
• Cocoa Computations in Commutative Algebra
• Singular is a Computer Algebra System for polynomial computations with special emphasis on the needs of commutative algebra, algebraic geometry, and singularity theory.
• Sage s a free open-source mathematics software system licensed under the GPL. It combines the power of many existing open-source packages into a common Python-based interface.

General Information

• commalg.org is... a website for the commutative algebra community. In addition to news items of interest to commutative algebraists, we list all the conferences we hear about that focus at least partially on commutative algebra, and sometimes some photos of them. We also maintain as complete a list of commutative algebraists as possible, and a huge list of links to websites of interest.
• CAIN Computer Algebra Information Network
• SymbolicNetSymbolic Mathematical Computation Information Center
• MathSciNet
• Wikipedia - The mathematics of Sudoku

Research Groups/Institutes

• RISC-LinzResearch Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria
• ORCCAOntario Research Centre for Computer Algebra, London, Ontario
• SCGSymbolic Computation Group, University of Waterloo, Ontario, Canada
• CoCoAResearch team in Genova, Italy
• ZCAZentrum für Computeralgebra, University of Kaiserslautern, Germany

Books (not updated)

• An Introduction to Grobner BasesWilliam W. Adams and Philippe Loustaunau, AMS, 1994
• Ideals, Varieties and Algorithms David Cox, John Little, and Donal O'Shea, Springer, 1992
• Using Algebraic Geometry David Cox, John Little, and Donal O'Shea, Springer, 1998
• Computational Commutative Algebra, I Martin Kreuzer, Lorenzo Robbiano, Springer, 2000
• Grobner Bases and Applications Bruno Buchberger and Franz Winkler, eds., Cambridge, 1998

Journals

• Journal of Symbolic Computation 
• The Journal of Software for Algebra and Geometry: Macaulay2