It's not just farms - the concept is known as a Cooperative, or Co-Op.
Collective
Right.
Yeomen
Yeoman
either state farms, consumer farms, corporate owned farms, or family owned farms
Yeoman farmers.
Hillshire Farms is owned by the Sara Lee Corporation
A group of shops all owned by one company is called a chain.
This system is often called "collectives". It was one of the prime goals of Vladamir Lenin.
Corporation
shareholders
Collective farms are a type of farm that are owned and operated as a joint enterprise by peasants. They are also known as communal farms.