Filtered algebra generally refers to structures in algebra where there is a filtration, which is a systematic way to impose a structure or hierarchy on the elements of the algebra. More formally, a filtered algebra is an algebra equipped with a filtration, which is an ascending chain of subalgebras indexed by a directed set. This can be useful in various branches of mathematics, particularly in homological algebra, algebraic topology, and representation theory. ### Definitions and Properties 1.
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