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.
References
Stanley decomposition Wikipedia(Text) CC BY-SA