Ciro Santilli @cirosantilli 37

Not to be confused with algebra over a field, which is a particular algebraic structure studied within algebra.

The degree of some algebraic structure is some parameter that describes the structure. There is no universal definition valid for all structures, it is a per structure type thing.

This is particularly useful when talking about structures with an infinite number of elements, but it is sometimes also used for finite structures.

Examples:

One of the defining properties of algebraic structure with two operations such as ring and field:This property shows how the two operations interact.

The order of a algebraic structure is just its cardinality.

Sometimes, especially in the case of structures with an infinite number of elements, it is often more convenient to talk in terms of some parameter that characterizes the structure, and that parameter is usually called the degree.