Primary Decomposition: Noetherian Ideal

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Page 3 of 4

Explores affine varieties, hypersurfaces, dimension in algebraic geometry, minimal prime ideals, and local properties of plane curves.

Explores Chinese idempotent constructions and their properties, including ideals and product characterization.

Explores the concept of fractions of rings and their uniqueness in ideals and quotients.

Explores ideals with finite sets of points and Hilberts Nullstellensatz in algebraic fields.

Explores Galois theory with a focus on Dedekind rings and their unique factorization of fractional ideals.

Covers the concept of prime ideals and local rings, emphasizing their importance.

Explores cyclotomic extensions, prime numbers, and ideal norms in number theory.

Discusses regular implicit functions, rings, ideals, sheaves, and ring operations.

Covers the concept of primary and secondary ideals, focusing on uniqueness and invariance properties.

Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.