In commutative algebra, a Stanley decomposition is a way of writing a ring in terms of polynomial subrings. They were introduced by .
Suppose that a ring R is a quotient of a polynomial ring k[x<sub>1</sub>,...] 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 x<sub>ñ</sub> is a monomial and each X<sub>ñ</sub> is a finite subset of the generators.