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Introduces affine varieties and covers morphisms between them and their coordinate rings.
Introduces projective, quasi-projective, and algebraic varieties, emphasizing the importance of regular functions in defining morphisms.
Covers modern algebraic geometry, including algebraic sets, morphisms, and projective algebraic sets.
Explores the construction of the field of rational functions on a variety and its connection with local rings and dimensions.
Explores morphisms, regularity, varieties, local rings, and evaluation morphism in algebraic geometry.
Explores the concept of the quotient in linearly reductive groups and varieties, discussing irreducibility, normality, and integral properties.
Explores algebraic varieties in linear algebra, focusing on their nature, determinants, irreducibility, prime properties, and geometric representation theory.
