Given central simple algebras "A" and "B", one can look at their tensor product "A" ⊗ "B" as a "K"-algebra (see tensor product of R-algebras). It turns out that this is always central simple. A slick way to see this is to use a characterization: a central simple algebra "A" over "K" is a "K"-algebra that becomes a matrix ring when we extend the field of scalars to an algebraic closure of "K". This result also shows that the dimension of a central simple algebra "A" as a "K"-vector space is always a square. The degree of "A" is defined to be the square root of its dimension.