16Z05 Computational aspects of associative rings (general theory)

Overview

16Z05 studies computational methods in associative algebra in computational aspects. It covers algorithmic and implementation-oriented questions for noncommutative algebra, including symbolic computation and effective structure calculations.

Related Wikipedia Page

Computational methods in associative algebra (Wikipedia)

Useful Links

• Computational methods in associative algebra (Wikipedia)
• Computer algebra system (Wikipedia)
• Algorithmic algebra (Wikipedia)

Key Ideas

• Canonical formulations and representative examples for computational methods in associative algebra
• How structural, local, and computational viewpoints interact in the subject
• Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in computer algebra, algorithmic classification, and explicit calculation with rings and modules.

Applications

• Computer algebra for ring computations
• Algorithmic classification of algebraic structures
• Symbolic methods in noncommutative algebra

References

• Buchberger, B. and Winkler, F. (eds.) (1998) Groebner Bases and Applications. Cambridge: Cambridge University Press.
• Cohen, H. (2000) A Course in Computational Algebraic Number Theory. 2nd edn. Berlin: Springer.

Recommended Textbooks

• SageMath documentation. Available online.
• Gathen, J. von zur and Gerhard, J. (2013) Modern Computer Algebra. 3rd edn. Cambridge: Cambridge University Press.