Explores discrete valuation rings, their properties, uniqueness of representation, and relationship with principal ideal domains.
Explores Dedekind rings, fractional ideals, integrally closed properties, prime ideal factorization, and the structure of fractional ideals as a commutative group.
Covers rings, modules, fields, minimal ideals, and the Nullstellensatz theorem.
Covers factorisation in PIDs, prime ideals, unique tuples, and common prime factors.
Covers a general introduction and discusses algebra, emphasizing the importance of unique factorization in algebraic structures.
Covers local Noetherian rings, integrally closed domains, discrete valuations, and fraction fields.
