In commutative algebra, a Rees decomposition is a way of writing a ring in terms of polynomial subrings. They were introduced by David Rees (1956).
Suppose that a ring R is a quotient of a polynomial ring k[x1,...] over a field by some homogeneous ideal. A Rees decomposition of R is a representation of R as a direct sum (of vector spaces)
where each ηα is a homogeneous element and the d elements θi are a homogeneous system of parameters for R and ηαk[θfα+1,...,θd] ⊆ k[θ1, θfα].
 | This commutative algebra-related article is a stub. You can help Wikipedia by expanding it. |
![{\displaystyle R=\bigoplus _{\alpha }\eta _{\alpha }k[\theta _{1},\ldots ,\theta _{f_{\alpha }}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9d628bd1a873bd519c797c79a1de2d16274a1707)