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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.
Covers the concept of localization and ideals in rings, focusing on extended and contracted ideals, integral extensions, and monic equations.
Explores the Chinese remainder theorem in commutative rings and ideals, demonstrating its applications and relevance in finding unique solutions.
Covers the proof of theorem 4.2 on multiplicities and the special structure of local rings at a simple point of a plane.
