Prime ideals and local rings

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Algebraic Subsets of A^1

Covers algebraic subsets of A^1 and ideals with a finite set of points.

Irreducible Factors and Noetherian Rings

Explores irreducible factors, Noetherian rings, ideal stability, and unique factorization in rings.

Rings and Ideals

Explores rings, domains, fields, and ideals, with a focus on constructions and properties.

Dedekind Rings: Theory and Applications

Explores Dedekind rings, integral closure, factorization of ideals, and Gauss' Lemma.

Hilberts Nullstellensatz and Ideals

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

Regular Implicit Functions

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

Separable Extensions: Dedekind Rings

Explores separable extensions and Dedekind rings, focusing on coefficients and prime ideals.

Primary Decomposition: Understanding Schemes

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.

Localization and Ideals

Covers the concept of localization and ideals in rings, focusing on extended and contracted ideals, integral extensions, and monic equations.

Factorisation in PIDs

Covers factorisation in PIDs, prime ideals, unique tuples, and common prime factors.