The Stacks project

Exercise 111.37.1. Give examples of graded rings $S$ such that

1. $\text{Proj}(S)$ is affine and nonempty, and

2. $\text{Proj}(S)$ is integral, nonempty but not isomorphic to ${\mathbf P}^ n_ A$ for any $n\geq 0$, any ring $A$.