Definition talk:Module Direct Product

There is

Module of All Mappings

Module Product

Module on Cartesian Product

Definition:Free Module Indexed by Set (which is needed to reformulate linear independence etc in a more practical way, and to rigorously introduce polynomials without resorting to tedious calculations)

The three proofs do special cases of the fact that a direct product of modules is a module. Interestingly, none of them does the general case. I suggest to keep one proof article that does the general case; the proofs in those particular cases are very very very similar anyway. The specific definitions themselves can go to the definition namespace.--barto (talk) 16:46, 4 December 2016 (EST)


 * Do the general case and then, if you must, add the proofs of the special cases with reference to the general case. --prime mover (talk) 16:47, 4 December 2016 (EST)

Left Modules
There was a reason to specify left modules in this definition.

An aborted attempt was made to define a tensor product as a construct involving both a left module and a right module, both of which had not been properly defined here. The original author expressed irritation at my insistence on defining all the entities in full and complete detail, and abandoned the project amid a cloud of bad feeling.

It was ever the intention to go back and fill in and distinguish between left direct products and right direct products, and the material is at a sort of half way house.

Please be aware that your work may endanger our attempts to make subtle distinctions between all the various types of object in this general area of mathematics, so please tread carefully here. --prime mover (talk) 17:55, 4 December 2016 (EST)