Engineering↗
Unique Factorisation
Handbook guide to Unique Factorisation, covering core definitions, key results, formulas, reasoning methods and worked examples in graduate abstract algebra.
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unique factorisation
Every page in the KEVOS library tagged unique factorisation. 5 pages.
Engineering↗
Ideals of the Maximal Order
Ideals and fractional ideals, unique factorisation into primes, and the group structure that makes the class group possible.
Engineering↗
The Ideal Class Group
The class group as the obstruction to unique factorisation, its finiteness, and what a complete computation must produce.
Engineering↗
Unique Factorisation Domains, Content and Primitive Parts
Content and primitive part, Gauss's lemma, and why factoring over the rationals reduces to factoring over the integers.
Engineering↗
Direct Products, Factor Congruences and Direct Indecomposability
Direct products, projection homomorphisms, factor congruences as the internal signature of a decomposition, directly indecomposable algebras and the limits of unique factorisation.
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