Recent content by sab47

Not so much, no. I've just heard of it. But I'll look into it.

Should I somehow show that any finitely generated set over Q has finite number of elements? Sorry to be so slow, like I said I'm self teaching these things. There must be a theorem or something about number of elements of finitely generated modules which I've forgotten!

number of elements? how do you mean?

Yes, but we're saying here that AB is singular here, so it doesn't have an inverse. Plus, finding inverse involves finding the determinant first...

there was a similar statement which said Q is not finitely generated over Z. So what I did with that was i said if we assume q1,...,qn generate Q. Then take a z in Z which is coprime with the denominator of all members of the generatind set (i.e coprime with all qi) then 1/z cannot be generated...

You've got to use determinants. That way you just map your matrices to set of real numbers R, and everything is just much easier ther!

Hey guys, I'm self-teaching maths to preper myself for the next term of uni, so I'm reading this book on abstract algebra, and somewhere it says that R (the set of real numbers) is not finitely generated as a module over Q (set of rational numbers). Now, I can see that it's not, but i can't...