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  In mathematics, a filtered algebra is a generalization of the notion of a graded algebra. Examples appear in many branches of mathematics, especially in homological algebra and representation theory. A filtered algebra over the field is an algebra over which has an increasing sequence of subspaces of such that and that is compatible with the multiplication in the following sense:
 In mathematics, a filtered algebra is a generalization of the notion of a graded algebra. Examples appear in many branches of mathematics, especially in homological algebra and representation theory. A filtered algebra over the field is an algebra over that has an increasing sequence of subspaces of such that and that is compatible with the multiplication in the following sense:

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  In mathematics, a filtered algebra is a generalization of the notion of a graded algebra. Examples appear in many branches of mathematics, especially in homological algebra and representation theory. A filtered algebra over the field is an algebra over which has an increasing sequence of subspaces of such that and that is compatible with the multiplication in the following sense:
 In mathematics, a filtered algebra is a generalization of the notion of a graded algebra. Examples appear in many branches of mathematics, especially in homological algebra and representation theory. A filtered algebra over the field is an algebra over that has an increasing sequence of subspaces of such that and that is compatible with the multiplication in the following sense:

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