Factorisation in Principal Ideal Domains

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

Explores idempotent elements, central orthogonal elements, commutative rings, and prime ideals in non-central rings.

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

Explores congruence relations in rings, principal ideals, ring homomorphisms, and the characteristic of rings.

Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.

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

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

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

Covers fundamental concepts in commutative algebra, including rings, units, zero divisors, and local rings.

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