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unique factorisation

4 resources tagged “unique factorisation” across the knowledge library.

4 items

Article7 Aug 2026Ideals of the Maximal OrderIdeals and fractional ideals, unique factorisation into primes, and the group structure that makes the class group possible.2 min readRead More Article7 Aug 2026The Ideal Class GroupThe class group as the obstruction to unique factorisation, its finiteness, and what a complete computation must produce.2 min readRead More Article7 Aug 2026Unique Factorisation Domains, Content and Primitive PartsContent and primitive part, Gauss's lemma, and why factoring over the rationals reduces to factoring over the integers.2 min readRead More Guide6 Aug 2026Direct Products, Factor Congruences and Direct IndecomposabilityDirect products, projection homomorphisms, factor congruences as the internal signature of a decomposition, directly indecomposable algebras and the limits of unique factorisation.4 min readRead More