If "A" is a finite-dimensional unital associative "K"-algebra, then "A"∗ is a finite-dimensional coalgebra, and indeed every finite-dimensional coalgebra arises in this fashion from some finite-dimensional algebra (namely from the coalgebra's "K"-dual). Under this correspondence, the commutative finite-dimensional algebras correspond to the cocommutative finite-dimensional coalgebras. So in the finite-dimensional case, the theories of algebras and of coalgebras are dual; studying one is equivalent to studying the other. However, relations diverge in the infinite-dimensional case: while the "K"-dual of every coalgebra is an algebra, the "K"-dual of an infinite-dimensional algebra need not be a coalgebra.