The PMBOK (5th edition, p. 558) defines a requirement as "a condition or capability that is required to be present in a product, service, or result to satisfy a contract or other formally imposed specification."
Scope and quality are categories of requirements. (See Juran on "Fit for Purpose".) Generally, scope refers to the functional requirements, and quality refers to the usability requirements.
The requirements documentation includes the requirements management plan and requirements traceability matrix. The requirements are also affected by the scope management plan and quality management plan.