Alphabeta MathHopf Modules, Coinvariants, and the Fundamental Theorem
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1 · Prerequisites
Abstract Algebra
- Binary Operations, Monoids, Groups and Subgroups
- Chain Conditions, Semisimple Modules and the Wedderburn–Artin Theorem
- Cosets, Index and Lagrange's Theorem
- Free Modules, Exact Sequences, Projective and Injective Modules
- Group Homomorphisms and the Isomorphism Theorems
- Modules, Submodules, Quotient Modules and the Isomorphism Theorems
- Normal Subgroups and Quotient Groups
- Rings, Subrings, Integral Domains and Fields
- Tensor Products of Modules
Categorification and Geometric Representation Theory
Linear Algebra
Real Analysis
2 · Logical flowchart
3 · Items
Definition
Right-right Hopf modules and coinvariants
Lemma
The coinvariants of a right-right Hopf module form a subspace
Lemma
The free right-right Hopf module on a vector space
Lemma
The coinvariant projection of a right-right Hopf module
Theorem
The fundamental theorem of right-right Hopf modules
Lemma
Coinvariants of a free right-right Hopf module
Corollary