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Filtration

A filtration of ideals of a commutative unit ring R is a sequence of ideals

... subset= I_2 subset= I_1 subset= I_0=R,

such that I_iI_j subset= I_(i+j) for all indices i,j. An example is the I-adic filtration associated with a proper ideal I of R,

... subset= I^3 subset= I^2 subset= I^1 subset= I^0=R.

A ring equipped with a filtration is called a filtered ring.

See also

Associated Graded Module, Associated Graded Ring, Rees Module, Rees Ring

This entry contributed by Margherita Barile

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Cite this as:

Barile, Margherita. "Filtration." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Filtration.html

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