A republic in English is a state without a monarch, but it also has a richer definition deriving from European antiquity and British constitutional history.
According to this definition, a republic is a Commonwealth or a form of government which pursues the public good through ethically committed institutions.
Oxford Dictionary definition of republic: A state in which the supreme power rests in the people and their elected representatives, or officers, as opposed to one governed by a king or similar ruler; a Commonwealth.
It is the people embodied, preserves it rights and which is regulated by laws, whatever may be the form of administration.
Accordingly, the republic is by no means the most perfect constitution, the deal state, which should exist everywhere it is capable of being implemented.
The US Constitution created a form of republican government that everybody calls a democratic republic. The people hold the ultimate power over the government through the election process, but all national policy decisions are made by elected officials.
Definition of republic