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).

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.

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