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Synonyms for Peremptory (same or very similar meaning)

WordNet sense 1 (offensively self-assured or given to exercising usually unwarranted power):
autocratic, bossy, magisterial, dominating, high-and-mighty

WordNet sense 2 (tending to domineer):
domineering

WordNet sense 3 (requiring attention or action):
imperative

WordNet sense 4 (determining or having the power to determine an outcome):
decisive


From the ODE community, based on WordNetadd/edit