i'll leave the "whys" for you to figure out!

set of all polynomials with coefficients in and of degree at most 1. this is an additive subgroup which is not closed under multiplication.

set of all constant functions or, if you want the subring to have the identity element of then would be an example.

(b) Find a subring of which is not an ideal. Why?

fix an and define this is a principal ideal.

(c) Find an ideal of which is not the zero ring or . Can this ideal be written as a principal idea? Why?

why?