Integral Domains and Abelian Groups

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Focuses on abelian p-groups, demonstrating technical results for classifying finite abelian groups.

Explores Frobenius theorems in number theory, ideal class groups, norm properties, and geometry of numbers.

Explores exact sequences of abelian group homomorphisms and provides examples.

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

Covers rings, modules, fields, minimal ideals, and the Nullstellensatz theorem.

Explores the properties of Euclidean domains, including gcd, lcm, and the Chinese remainder theorem for polynomial rings.

Explores finitely generated abelian groups, focusing on their structure and isomorphism theorems.

Explores the properties and structure of Sylow subgroups in group theory, emphasizing a theorem-independent approach.

Explores torsion and divisibility in abelian groups, including p-divisible groups and their contrast with torsion elements.

Covers the properties of Euclidean domains and irreducible elements in polynomial rings.