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From DuckDuckGo:

1. An economic system in which the means of production and distribution are privately or corporately owned and development occurs through the accumulation and reinvestment of profits gained in a free market.

2. An economic system based on predominantly private (individual or corporate) investment in and ownership of the means of production, distribution, and exchange of goods and wealth; contrasted with socialism or especially communism, in which the state has the predominant role in the economy.

3. A socio-economic system based on private property rights, including the private ownership of resources or capital, with economic decisions made largely through the operation of a market unregulated by the state.

4. A socio-economic system based on the abstraction of resources into the form of privately-owned capital, with economic decisions made largely through the operation of a market unregulated by the state.

5. A specific variation or implementation of either such socio-economic system.

6. An economic system based on private ownership of capital.

This isn't necessary for all of them, but from Wikipedia:

A state is a political entity that regulates society and the population within a territory.

Slave masters are regulators of population, so they are an actor of the state.