Let R be field of real numbers and R[x] the ring of polynomials in x with coefficients in R. Which of the following subsets of R[x] is a subring of R?
I) All polynomials whose coefficient of x is zero.
II) All polynomials whose degree is even integer, together with zero polynomial.
III) All polynomials whose coefficient are rational numbers.
THE ANSWER SAYS ONLY I AND III ARE CORRECT.
I DON'T GET WHY II IS NOT CORRECT.
--ITS COMPLETE IN ADDITION
--IT HAS IDENTITY ELEMENT ZERO
--FOR EVERY POLYNOMIAL THERE IS AN ADDITIVE INVERSE WHICH WILL ALSO HAVE EVEN DEGREE
--ALSO ADDITION IS ABLIAN
--ITS COMPLETE IN MULTIPLICATION
--ITS ASSOCIATIVEI IN MULTIPLICATION