User:Barto

Modules

 * Organize Direct Product of Modules is Module, Finite Direct Product of Modules is Module, Module on Cartesian Product, Vector Space of All Mappings
 * Consider renaming Definition:Free Module Indexed by Set to something less pedantic (name is used in some other articles; better decide quickly before there are more)

Direct Product and Direct Sum
and the naming of those subdefinitions should be consistent: Finite Case, General Case or something like that.
 * Be consistent in the use of product and sum: product is the primary notion, sum is derived from it.
 * Make sure that all definition pages include a definition for arbitrary families. Ideally, there should be:
 * A definition for two components
 * A definition for any finite number of components
 * A definition for general families
 * (Optionally: a definition for countable families)
 * Be consistent with page titles: External Direct Sum of X's vs. Direct Sum of X's vs. X Direct Sum. Examples: Definition:External Direct Sum of Rings, Definition:Ring Direct Sum
 * Try to remove the "external" where it's superfluous and unnecessarily pedantic. Also, there is sometimes ambiguity, e.g. in Definition:Ring Direct Sum -> internal or external? it's not clear from the title. External is the most common and is usually understood if nothing is specified.

Support

 * Rethink how to structure the different notions

Polynomials

 * Clean up Definition:Polynomial (Abstract Algebra)
 * Add a definition using Definition:Monoid Ring

Modules

 * Define modules and unitary modules using Definition:Endomorphism Ring of Abelian Group, see Morphism to Endomorphism Ring Defines Module
 * 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.

Definition-level

 * Free Module Indexed by Set is Free
 * Canonical Basis of Free Module Indexed by Set is Basis
 * Universal Property of Free Modules
 * Universal Property of Direct Product of Modules
 * Universal Property of Direct Sum of Modules
 * Endomorphism Ring of Abelian Group is Ring

Spaces of Morphisms

 * Definition:Group of Homomorphisms between Abelian Groups
 * Definition:Endomorphism Ring of Abelian Group
 * 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