I hate the term "vector space"
Will you agree with me to only say...
R-linear space
R-module
no I like unergonomic terminology
going forward?
Every vector space is an r module sure but every r module isn't a vector space??
That's like saying I don't like squares they're all rectangles anyways so imma call em that
There's more information there that's lost when you call it a module
I think I've phrased my advocacy in a bad way. It just feels weird to me to have just a radically different looking name for an object obtained by adding an extra condition on a module. It feels like if we woke up and decided to call "abelian groups" something like "symmetry booklets" for some reason, rather than thinking of them as groups satisfying extra properties and naming them in accordance with that schema. A "vector space" to me should be an "<ADJECTIVE> module".
Maybe something like "tame module" or "fieldic module" or "fielded module"
I like the "extra conditions should just be extra adjectives" philosophy on first glance, but if we take it seriously then don't we have to give up "field" (and so presumably "fielded" and "fieldic") too? That's a radically different looking name for a commutative division ring.






















