User:Barto

Modules

 * Define modules and unitary modules using Definition:Endomorphism Ring of Abelian Group, see Morphism to Endomorphism Ring Defines Module
 * Consider merging Direct Product of Modules is Module, Module Product, Module on Cartesian Product

Basises and their properties

 * Free Module Indexed by Set is Free proof
 * Canonical Basis of Free Module Indexed by Set is Basis proof
 * Universal Property of Free Modules proof
 * Universal Property of Direct Product of Modules proof
 * Universal Property of Direct Sum of Modules proof
 * Determining Definition:Multilinear Mapping using basises, use this in Definition:Monoid Ring
 * Correspondence between Definition:Multilinear Mapping and linear maps to Definition:Module of Multilinear Mappings.

Polynomials

 * Define them elegantly in full generality using Definition:Monoid Ring

Spaces of Morphisms

 * Definition:Group of Homomorphisms between Abelian Groups
 * Definition:Endomorphism Ring of Abelian Group is Ring proof
 * Definition:Module of Homomorphisms between Modules
 * Definition:Module of Multilinear Mappings
 * Definition:Endomorphism Ring of Module
 * Note that there is already a general Definition:Group of Automorphisms for algebraic structures with one operation.

Other useful notions

 * Definition:Support of Element of Direct Product (of algebraic structures with unique unity, e.g. monoids), Definition:Finite Support
 * Definition:Substructure of Elements of Finite Support or something, use this in Definition:Module Direct Sum or even
 * Substructure of Elements of Finite Support is Closed