Editing Abstract Algebra (section)

== <span style="color: #FFFFFF;">Creating</span> ==
Advanced algebra research directions:
# '''Representation theory''': study groups through their actions on vector spaces (linear representations); key to quantum mechanics and the Standard Model.
# '''Homological algebra''': study algebraic structures through chain complexes and their cohomology; the language of modern topology and algebraic geometry.
# '''Category theory''': the most abstract unification — study of mathematical structures through maps between them, independent of what the objects "are".
# '''Computational algebra''': algorithms for polynomial factorization (Berlekamp, Cantor-Zassenhaus), Gröbner bases (Buchberger algorithm), and group computation (Schreier-Sims).
# Design of post-quantum cryptographic systems based on algebraic structures hard to attack with quantum algorithms.

[[Category:Mathematics]]
[[Category:Abstract Algebra]]
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