The Stacks project

Exercise 111.49.8. On a separated scheme $X$ of finite type over a field: Give an example of a Cartier divisor which is not the difference of two effective Cartier divisors. Hint: Find some $X$ which does not have any nonempty effective Cartier divisors for example the scheme constructed in [III Exercise 5.9, H]. There is even an example with $X$ a variety – namely the variety of Exercise 111.49.9.