In mathematics, an algebraic structure consists of a nonempty set A
(called the underlying set, carrier set or domain),
a collection of operations on A of finite arity (typically binary operations),
and a finite set of identities, known as axioms, that these operations must satisfy.
An algebraic structure may be based on other algebraic structures with operations
and axioms involving several structures.
For instance, a vector space involves a second structure called a field,
and an operation called scalar multiplication between elements of the field
(called scalars), and elements of the vector space (called vectors).
Wiki
|