kompleksalgebra
Kompleksalgebra is a mathematical structure consisting of a complex vector space equipped with a bilinear multiplication into itself, making it an algebra over the field of complex numbers. If the multiplication is associative, it is called an associative complex algebra; if it also has a multiplicative identity, it is a unital complex algebra. The scalar multiplication by complex numbers is compatible with the algebra multiplication, so (αa)b = α(ab) = a(αb) for all α in C and a,b in A. The center typically contains the image of C, and many authors view A as a C-algebra.
Common examples include the complex numbers C themselves, viewed as a complex algebra; the matrix algebra M_n(C);
Complex algebras may be commutative or noncommutative, and they can be finite- or infinite-dimensional. They play