Final answer:
A confederation or confederal system is a type of government where the primary powers are held at the state level without a president, with states retaining significant independence.
Step-by-step explanation:
The term that identifies a state-centered, decentralized government where the primary powers of government are held at the state level with no president is called a confederation or confederal system. In this type of system, the central authority has limited power, and the constituent states retain a large degree of sovereignty and independence. An example of a confederation was the United States under the Articles of Confederation, before the adoption of the current Constitution. In more modern times, the European Union can be described as a sort of confederation, with member states having significant control over their affairs but cooperating on certain issues of common interest.