6 Answered Questions for the topic Abstract Algebra
Let (G, *) be a group. Prove that the map π : G → G defined by π(g) = g * g is a homomoprhism if and only if G is abelian
Let (G, *) be a group. Prove that the map π : G → G defined by π(g) = g * g is ahomomoprhism if and only if G is abelian
Abstract Algebra Algebra
Prove that if R is a ring and I ▹ R, then R[x]/I [x] ≃ (R/I )[x] for any indeterminate x.
Must eigenvalues be numbers?
This is more a conceptual question than any other kind. As far as I know, one can define matrices over arbitrary fields, and so do linear algebra in different settings than in the typical... more
Help me focus my study for the GRE math subject exam?
I'm preparing for the GRE Math Subject test, but I'm at a bit of a disadvantage, having never taken an algebra class or a probability class. Obviously I'm not going to learn a semester of abstract... more
Irreducible but not prime element?
>I am looking for a ring element which is irreducible but not prime. So necessarily the ring can't be a PID. My idea was to consider $R=K[x,y]$ and $x+y\\in R$. This is irreducible because in... more