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)
:
where each ''x''
''α'' is a monomial and each ''X''
''α'' is a finite subset of the generators.
See also
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Rees decomposition In commutative algebra, a Rees 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
Field may refe ...
*
Hironaka decomposition In mathematics, a Hironaka decomposition is a representation of an algebra over a field as a finitely generated free module over a polynomial subalgebra or a regular local ring. Such decompositions are named after Heisuke Hironaka, who used this in ...
References
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Commutative algebra
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