Filter (mathematics)
Linear filters

A linear (ultra)filter is an (ultra)filter on the lattice of vector subspaces of a given vector space, ordered by inclusion. Explicitly, a linear filter on a vector space X is a family B of vector subspaces of X such that if A, B ∈ B and C is a vector subspace of X that contains A, then A ∩ B ∈ B and C ∈ B.

A linear filter is proper if it does not contain { 0 }.
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