Primary Decomposition: Understanding Schemes

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Geometric Objects in Algebra

Covers the study of graded modules and quasicoherent sheaves in algebraic geometry.

Galois Theory: Dedekind Rings

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

Factorisation in PIDs

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

Factorisation in Dedekind Ring

Explains the factorisation of ideals in a Dedekind ring using prime ideals and covers ramification index, residual fields, inertia degree, and properties of Dedekind rings.

Additivity of Dimension & Height

Explores the additivity of dimension and height in a finitely generated k-algebra domain, showcasing its applications and implications.

Ring Operations: Ideals and Classes

Covers the operations in rings, ideals, classes, and quotient rings.

Affine Algebraic Varieties: Zariski Topology

Explores affine algebraic varieties, emphasizing the Zariski Topology and regular functions.

Projective Morphisms: Theory and Applications

Explores projective morphisms, graded modules, and their applications in algebraic geometry, emphasizing their properties and construction.

Ideals and Representations

Covers ideals, representations, modules, and maximal ideals in associative algebras.

Cyclotomic Extensions: Norms, Ideals, and Primes

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