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I think one should mention an important generalization of this construction (also called the Rees algebra) that applies to any (associative) algebra with a (decreasing or increasing) filtration. (In the commutative case, this gives generalized blowups and tangent cones for decreasing filtrations, and generalized asymptotic cone for increasing ones.) Math MisterY (talk) 11:50, 10 November 2021 (UTC)