Rees decomposition
In commutative algebra, a Rees decomposition is a way of writing a ring in terms of polynomial subrings. They were introduced by {{harvs|txt|last=Rees|first=David|authorlink=David Rees (mathematician)|year=1956}}.
Definition
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].
See also
References
- {{citation|mr=0074372
|last=Rees|first= D.
|title=A basis theorem for polynomial modules
|journal=Proc. Cambridge Philos. Soc.|volume= 52 |year=1956|pages= 12–16}}
- {{citation|mr=1122013
|last=Sturmfels|first= Bernd|last2= White|first2= Neil
|title=Computing combinatorial decompositions of rings
|journal=Combinatorica |volume=11 |year=1991|issue= 3|pages= 275–293|doi=10.1007/BF01205079}}
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