Stanley decomposition
In commutative algebra, a Stanley decomposition is a way of writing a ring in terms of polynomial subrings. They were introduced by {{harvs|txt|last=Stanley|first=Richard|authorlink=Richard P. Stanley|year=1982}}.
Definition
Suppose that a ring R is a quotient of a polynomial ring k[x1,...] over a field by some ideal. A Stanley decomposition of R is a representation of R as a direct sum (of vector spaces)
:
where each xα is a monomial and each Xα is a finite subset of the generators.
See also
References
- {{citation|mr=0666158
|last=Stanley|first= Richard P.
|title=Linear Diophantine equations and local cohomology
|journal=Invent. Math. |volume=68 |year=1982|issue= 2|pages= 175–193|doi=10.1007/bf01394054}}
- {{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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