Properties which do not pass to classical rings of quotients

We construct examples of Ore rings satisfying some standard ring-theoretic properties for which the classical rings of quotients do not satisfy those properties. Examples of properties which do not pass to rings of quotients include: Abelian, Dedekind-finite, semicommutative, 2-primal, and NI. In the process of constructing these examples we correct the literature. We also introduce two important construction techniques.