Stanley decomposition explained

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

Definition

Suppose that a ring R is a quotient of a polynomial ring k[''x''₁,...] over a field by some ideal. A Stanley decomposition of R is a representation of R as a direct sum (of vector spaces)

R = o plus _{\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