abstract algebra
The lecturer said I was reading in the wrong place and that we aren't doing any work on quadratic integer rings - and that to determine that 3 is irreducible in Q[i sqrt(5)] requires a "field norm."
I've been able to do a lot of my HW, but I've got a problem in the chapter I'm working on - to prove x^3 + nx + 2 is irreducible for n != -1, 3 or 5. I'm beginning to wonder why we're using this book since it doesn't specify over what ring we're working? Don't all 3d degree polynomials have a root in C? Are they not thus reducible in C? Then does the book mean over Q? over Z? I'm working on "field extensions".
I've been able to do a lot of my HW, but I've got a problem in the chapter I'm working on - to prove x^3 + nx + 2 is irreducible for n != -1, 3 or 5. I'm beginning to wonder why we're using this book since it doesn't specify over what ring we're working? Don't all 3d degree polynomials have a root in C? Are they not thus reducible in C? Then does the book mean over Q? over Z? I'm working on "field extensions".