Covers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.
Covers modern algebraic geometry, including algebraic sets, morphisms, and projective algebraic sets.
Covers the concept of morphism of groups, actions on sets, and automorphisms.
Introduces affine varieties and covers morphisms between them and their coordinate rings.
Explores algebraic varieties in linear algebra, focusing on their nature, determinants, irreducibility, prime properties, and geometric representation theory.
Explores the construction of the field of rational functions on a variety and its connection with local rings and dimensions.
Delves into advanced group theory concepts such as isomorphisms and homomorphisms.
Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.
Covers concrete categories with sets and structures, including Ens, Gr, Ab, and Vectk.
Introduces projective, quasi-projective, and algebraic varieties, emphasizing the importance of regular functions in defining morphisms.
Explores the dimension of algebraic varieties, including the (Krull)-dimension of rings and computing dimensions using tools from commutative algebra.
