Synonyms for Prerequisite:

adj.

necessary (adjective)
important, essential, expedient, indispensable, imperative, required, mandatory, vital, requisite, obligatory.
required (adjective)
obligatory, necessary, involuntary, Stipulated, essential, inexorable, binding, imperative, inevitable, required, inescapable, requisite, compulsory, indispensable, proviso, mandatory, pressing, constraining, must.

n.

element, basis, concern, essence, core, priority, feature, burning issue/question, staple, key. apprenticeship, correspondence course, class, articles, sine qua non, need, precondition, day school, crash course, ed, concentration, course, doctoral. cognition (noun)
requirement.
condition (noun)
precondition, sine qua non.
condition, necessity (noun)
need, must, precondition, requirement, sine qua non.
essential (noun)
expedient, important.
necessary (noun)
basic, at all costs, of necessity, vital, without fail.
requirement (noun)
inevitability, compulsion, condition, inexorability, constraint, obligation, mandate, stipulation, requirement, necessity.

Other synonyms:

precondition, sine qua non. need. Other relevant words:
course, precondition, apprenticeship, doctoral, basic, vital, feature, sine qua non, concentration, staple, basis, priority, important, essence, articles, need, core, element, class, expedient, concern, ed, key.