Covers the concept of ideals in polynomial rings and their properties.
Explores the concept of fractions of rings and their uniqueness in ideals and quotients.
Explores primary decomposition and schemes in algebraic geometry, emphasizing the importance of working over non-algebraically closed fields and the concept of fibers of morphisms.
Explores the dimension of algebraic varieties, including the (Krull)-dimension of rings and computing dimensions using tools from commutative algebra.
Covers the proof of theorem 4.2 on multiplicities and the special structure of local rings at a simple point of a plane.
