Structure theorem for finitely generated modules over a principal ideal domain

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Explains submodules, generated modules, and ring ideals in module structure.

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Covers a general introduction and discusses algebra, emphasizing the importance of unique factorization in algebraic structures.

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

Factorisation in PIDs

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

Integral Domains: Factorisation and Noetherian Rings

Explores factorisation in Principal Ideal Domains and Noetherian rings, emphasizing the integral closure concept and the factorisation of ideals in Dedekind rings.

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

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Covers the concepts of ideals, principal ideal domains, and ring homomorphisms.

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