Let D be a 1-dimensional Prüfer domain with exactly two maximal ideals. We completely determine the star operations and the semistar operations on D. Let G be a torsion-free abelian additive group. If G is not discrete, G is called indiscrete. If every non-empty subset S of G which is bounded below has its infimum inf(S) in G, then G is called complete. If G is not complete, G is called incompl...