|Jan13-13, 01:35 PM||#1|
From my textbook:
A free R-module is "A left R-module F is called a free left R-module if F is isomorphic to a direct sum of copies of R..."
I know that another definition of an R-module a module with a basis...but I don't know how to connect that definition with this one. Also, what does "copies of R" mean?
Thanks in advance
|Jan21-13, 02:51 AM||#2|
This is the underlying abelian group (analogous to vectors in vector space), and it looks like there is a natural way to multiply on the left by elements of R (analogous to scalars in a vector space).
So that seems to suggest that a left R-module does indeed have a basis. Now let's consider if we think a left R-module with a basis is a free module. Uh, never mind, I'll leave that for someone else
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