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What is (abstract) Algebra?

Algebra: representation theory, Hopf algebras, quantum groups;

Category theory: monoidal categories;

Mathematical Physics: conformal field theories

Theory of Rings and Modules.

Noncommutative rings and their modules, algebraic coding theory.

Group theory, representation theory of groups, abstract finite groups.

Multivariate Public Key Cryptography, Symbolic Computation, Abstract Algebra, Coding Theory

Noncommutative ring theory, homological algebra, applied linear algebra.