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)

$R=\underset{\alpha }{⨁}{x}_{\alpha }k(X_{\alpha })$

where each x_α is a monomial and each X_α is a finite subset of the generators.

See also

• Rees decomposition
• Hironaka decomposition