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Tag: rings-and-modules
29 items with this tag.
Apr 17, 2026
01. Rings - Definition and Examples
rings-and-modules
Apr 17, 2026
02. Basic Properties
rings-and-modules
Apr 17, 2026
03. Ideals and Quotients
rings-and-modules
Apr 17, 2026
04. Prime and Maximal Fields, Euclidean Domains and PIDs
rings-and-modules
Apr 17, 2026
05. An Introduction to Fields
rings-and-modules
Apr 17, 2026
06. Unique Factorisation
rings-and-modules
Apr 17, 2026
07. Modules - Definitions and Examples
rings-and-modules
Apr 17, 2026
08. Quotient Modules and the Isomorphism Theorems
rings-and-modules
Apr 17, 2026
09. Free, Torsion and Torsion-Free Elements
rings-and-modules
Apr 17, 2026
10. Canonical Forms for matrices over Euclidean Domain
rings-and-modules
Apr 17, 2026
11. Presentations and Canonical Form for Modules
rings-and-modules
Apr 17, 2026
12. Application to Rational and Jordan Canonical Forms
rings-and-modules
Apr 17, 2026
01 - Ring Structure of Quotient Group
rings-and-modules
Apr 17, 2026
02 - Universal Property of Quotients
rings-and-modules
Apr 17, 2026
03 - Direct Sum Decomposition of Quotients
rings-and-modules
Apr 17, 2026
04 - Principal Ideal Domain are Unique Factorisation Domains
rings-and-modules
Apr 17, 2026
05 - Ring of Polynomials with Integer Coefficients is a UFD
rings-and-modules
Apr 17, 2026
06 - UFD Property of Polynomial Ring
rings-and-modules
Apr 17, 2026
07 - Universal Property of Quotients
rings-and-modules
Apr 17, 2026
08 - Smith Normal Form
rings-and-modules
Apr 17, 2026
09 - Structure Theorem for Finitely Generated Modules over a Euclidean Domain
rings-and-modules
Apr 17, 2026
01 - Rings
rings-and-modules
lemma
Apr 17, 2026
02 - Fields
rings-and-modules
lemma
Apr 17, 2026
03 - Integral Domains
rings-and-modules
lemma
Apr 17, 2026
04 - Ideals
rings-and-modules
lemma
corollary
Apr 17, 2026
05 - Quotients
rings-and-modules
Apr 17, 2026
06 - Isomorphism Theorems
rings-and-modules
corollary
Apr 17, 2026
07 - Modules
rings-and-modules
lemma
corollary
Apr 17, 2026
08 - Matrix Representations
rings-and-modules
corollary
lemma