Dave Rusin <email@example.com> wrote: > >Yeah, sure. A vector space is a module over a field. That's absolutely >true and probably given that way in Bourbaki somewhere, but even in >selective institutions I can't believe students learn about modules >before vector spaces. Is there really a source anywhere that pretends to >_introduce_ vector spaces in terms of abelian groups?
Er.. yeah. MacLane and Birkhoff, Algebra, 3rd ed. 1988.
Chapter 5 Modules "An R-module is an additive abelian group together with a function..."
Chapter 6 Vector Spaces "A vector space is a module over a field F."
I don't know if teachers actually use this as a textbook for an undergrad class though.