Algebraic geometry Anneaux (Algèbre) Artinian rings and modules, finite-dimensional algebras Associative rings and algebras Categories and geometry Category theory; homological algebra Chain conditions, finiteness conditions Characteristic $p$ methods (Frobenius endomorphism) and reduction to characteristic $p$; tight closure Commutative algebra Foundations General commutative ring theory Group theory and generalizations Linear algebraic groups and related topics Noncommutative algebraic geometry Presheaves and sheaves Projective and free modules and ideals Rings (Algebra) Special categories Structure theory Theory of modules and ideals Topoi