This entry is about rings which mimic the composition operation on endo-functions on the ground ring. For the unrelated notion of algebras mimicking the composition of sums of squares see at composition algebra.
The notion of composition rings is an abstraction of the structure present in a ring of functions from the ground ring to itself: In addition to (pointwise) addition and multiplication, there is a compatible operation of composition.
A composition ring is a commutative ring equipped with an operation
such that for all elements , , and , we have:
,
,
(associativity of composition).
The endo]-[[function algebra on a commutative ring is a composition ring, with “” being the composition of functions.
In particular, every polynomial ring is a composition ring with “” being the actual composition of polynomials regarded as functions from the ground ring to itself.
Every commutative ring becomes a composition ring by setting .
The concept is due to:
See also:
Wikipedia, Composition ring
Erhard Aichinger, The Structure of Composition Algebras(1998) pdf
Last revised on August 21, 2024 at 01:45:29. See the history of this page for a list of all contributions to it.