Algebra is the study of sets and their operations. "High school algebra" is usually limited to the study of real numbers and the operations of addition and mul

Algebra is the study of sets and their operations. "High school algebra" is usually limited to the study of real numbers and the operations of addition and multiplication. In upper division undergraduate mathematics, you learn about other kind of algebras. For example, there is the set of regular polygons with operations such as rotation and reflection. In OO, a class of objects defines the operations (methods) that are valid, and thus, a class is an algebra, and a set of classes is a family of algebras. I suppose that you would need a form of multiple-inheritance in order to have a family of algebras for an object.