Stanley decomposition

In commutative algebra, a Stanley decomposition is a way of writing a ring in terms of polynomial subrings. They were introduced by Richard Stanley (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.

gollark: haskell.haskell(haskell(haskell, haskell)(haskell))
gollark: why.wouldYou(want.that())
gollark: I bet there's an extension for it.
gollark: You can get pi *zeros* cheaply, at least, but micro-SD cards are annoying.
gollark: Also honestly not that good compared to other SBCs except in the area of community support.

See also

References
  • Stanley, Richard P. (1982), "Linear Diophantine equations and local cohomology", Invent. Math., 68 (2): 175–193, doi:10.1007/bf01394054, MR 0666158
  • Sturmfels, Bernd; White, Neil (1991), "Computing combinatorial decompositions of rings", Combinatorica, 11 (3): 275–293, doi:10.1007/BF01205079, MR 1122013
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