Engineering↗
Dedekind Domains: Ideal Factorisation and Arithmetic
Handbook guide to dedekind domains: ideal factorisation and arithmetic with core definitions, structural results, reasoning methods and verification checks.
Tag
ideal
Every page in the KEVOS library tagged ideal. 10 pages.
Engineering↗
Division-Norm Rings and Principal Ideal Methods
Handbook guide to division-norm rings and principal ideal methods, covering definitions, key results, methods, verification checks and worked examples.
Engineering↗
Maximal and Prime Ideals
Handbook guide to maximal and prime ideals with core definitions, structural results, reasoning methods and verification checks.
Engineering↗
Modules over Principal Ideal Domains
Handbook guide to modules over principal ideal domains, covering definitions, key results, methods, verification checks and worked examples.
Engineering↗
Multivariable Division and Polynomial Ideal Reduction Bases
Handbook guide to multivariable division and polynomial ideal reduction bases, with definitions, key results, methods, verification checks and worked.
Engineering↗
p-adic Numbers and Valuations
Handbook guide to p-adic numbers and valuations with core definitions, structural results, reasoning methods and verification checks.
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↗
Boolean Rings and the Boolean Algebra-Ring Correspondence
Boolean rings, the mutual translation with Boolean algebras, term equivalence as the precise relationship, and why the ring picture makes ideals and the prime spectrum available.
Engineering↗
Filters, Ideals and Ultrafilters
Filters and ideals on a Boolean algebra, principal and free filters, ultrafilters and their three equivalent characterisations, and the role of ultrafilters throughout the rest …
Engineering↗
Orders and Ideals in Number Fields
Orders, the maximal order, fractional and integral ideals, unique factorisation of ideals in a Dedekind domain, ideal arithmetic by Hermite normal form, and the two-element repr…
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