So I like to get down into the details of how certain mathematical concepts came to be, and purely as a matter of curiosity, I was wondering if anyone know which mathematician first gave the definition of a direct sum?
I’ve always just sort of assumed that since for a finite set of modules, the direct sum and the direct product is the same, people probably came up with the direct product first, and then later, some mathematician wanted to do something with infinite sets of modules, realized that the universal property (of direct sums) doesn’t necessarily hold in that case, and so invented the direct sum to ”get around this,” but I’ve been wondering whether we actually know that this is what happened.
Any takers?