Hello, this questions came up in my exam and I was wondering if I got it right!
TRUE or FALSE:
Every field of 16 elements is commutative
I said TRUE since if we take a field minus the 0 element, then we have a group of units of order 15, which is cyclic and hence abelian by Sylow theory! So if we put the zero element back in clearly that commutes with everything too. Is this correct?
I also said that R[X] was a subring of C[X] , ie. real polynomials are a subring of complex polynomials, is this correct? Thanks for any advice