I am reading Sharp: Steps in Commutative Algebra, Chapter 2: Ideals. (see attached pages 18-19 for Sharp's definitions etc)
On page 19 Sharpe gives the following exercise
Let X be an indeterminate and consider the ring [X] of polynomials in X with co-efficients in
(i) an example of a subring of [X] which is not an ideal of [X]
(ii) an example of an ideal of [X] which is not a subring of [X]
I would appreciate help with this exercise.