Originally Posted by
elninio How exactly does this read:
(prove that) R[x]/<x^2+2> (is isomorphic to C)
It reads:
(prove that) the quotient ring of
[the ring of polynomials with real coefficients] by the ideal generated by
(is isomorphic to
To prove this, given any use the division algorithm to write where and are uniquely determined by Define a map by All that remains is to show that is a ring epimomophism (surjective homomorphism) with kernel
Originally Posted by
elninio And what exactly does the "/" imply algebraicly?
In general if is a ring and is an ideal of denotes the quotient ring of by :
where given a fixed denotes the additive coset