Ring homomorphisms Algebraic structures Related structures Algebraic number theory Noncommutative algebraic geometry Free algebra Clifford algebra In mathematics, a composition ring, introduced in (Adler 1962), is a commutative ring (R, 0, +, −, ·), possibly without an identity 1 (see non-unital ring), together with an operation such that, for any three elements
) has any algebraic relationship to
There are a few ways to make a commutative ring R into a composition ring without introducing anything new.
More interesting examples can be formed by defining a composition on another ring constructed from R. For a concrete example take the ring
, considered as the ring of polynomial maps from the integers to itself.
A ring endomorphism of
Therefore, one may consider the elements
as endomorphisms and assign
One easily verifies that
satisfies the above axioms.
, and also to the subring of all functions
formed by the polynomial functions.